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Topic: Penman equation

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	Penman equation - Wikipedia, the free encyclopedia
		The Penman equation describes evaporation (E) from an open water surface.
		It was developed by Michael Penman from Kelso in his laboratory.
		There are numerous versions of the Penman equation, one of which is:
	en.wikipedia.org /wiki/Penman_equation (122 words)

	Penman- Monteith Derivation
		This is the Penman-Monteith equation for evaporation from a wet surface.
		Equation 16 is the Penman-Monteith equation for a leaf.
		We are assuming that the surface is wet and the surface temperature is approximately equal to the wet-bulb temperature.
	biomet.ucdavis.edu /evapotranspiration/PMDerivation/PMD.htm (1086 words)

	The Garden with Insight garden simulator v1.0: Hydrology - Evapotranspiration
		The slope of the saturation vapor pressure curve is estimated with the equation [Equation 54].
		The surface roughness is estimated with the equation [Equation 68] and the crop displacement height is estimated with the equation [Equation 69] where CHT is crop height in m.
		The canopy resistance is computed with the equation [Equation 71] where p(1) is a parameter ranging from 1.0 to 2.0, LAI is the leaf area index of the crop, g*(o) is the leaf conductance in m/sec, and CO2 is the carbon dioxide level in the atmosphere in ppm.
	www.gardenwithinsight.com /help100/00000260.htm (1941 words)

	New Page 1
		Penman combined energy balance and aerodynamic equations into what is commonly known as the "combination equation" which is now used extensively throughout the world.
		Later Penman (1963) indicated that the two stage process water short grass could be obtained directly by using alfa = 0.25 and using 1 instead of 0.5 in the wind term.
		*Penman defined potential evaporation as evaporation from a fresh green crop, of about the same color as grass, completely shading the ground, of fairly uniform height, and never short of water.
	web.nmsu.edu /~yikemura/Penman/method.htm (791 words)

	ET003
		The Hargreaves and Samani equation requires only the location latitude and daily maximum and minimum temperature to estimate ETo, whereas the Penman equation requires the location latitude, maximum and minimum temperature, maximum and minimum relative humidity, daily mean wind speed, and an estimate of net radiation from percentage cloud cover.
		The wind speed was varied from 2.0 to 10 mph using zero percent cloud cover to illustrate the effect of wind speed on the Penman equation and the lack of effect on the Hargreaves and Samani equation.
		Equations 1, 2, and 3 are used to calculate saturation vapor pressure at the dewpoint, maximum, and minimum temperatures, respectively (Tetens', 1930).
	biomet.ucdavis.edu /evapotranspiration/NWSETo/NWSETo.htm (896 words)

	Evapotranspiration - Wikipedia, the free encyclopedia
		The most general and widely used equation for calculating ET is the Penman equation.
		The simpler Blaney-Criddle equation was popular in the Western United States for many years but it is not as accurate in regions with higher humidities.
		PET is higher in the summer, on less cloudy days, and closer to the equator, because of the higher levels of solar radiation that provides the energy for evaporation.
	en.wikipedia.org /wiki/Evapotranspiration (973 words)

	[No title]
		In Equation 4.1, S is surplus, P is precipitation, E is evaporation, w is soil moisture, and t is time.
		Penman's derivation eliminates the need for measuring water surface temperature; only the air temperature is required.
		Both the Slatyer-McIlroy and the Priestley-Taylor definitions consider the radiation term in the Penman equation to be a lower limit for the evaporation from a moist surface.
	www.crwr.utexas.edu /reports/1997/rpt97-1/SECT4.HTM (4073 words)

	HESS - Abstract
		It is shown that this upper limit is perfectly defined and is given by the Penman equation, applied with the corresponding meteorological data (incoming radiation and air characteristics measured at a reference height) and the appropriate surface characteristics (albedo, roughness length, soil heat flux).
		Although the potential evaporation from a given surface is readily calculated from the Penman equation, its physical significance or interpretation is not so straightforward, because it represents only an idealized situation, not a real one.
		If they are taken at a height of 2 m (the height of the meteorological observations), the dimension of the saturated surface in the direction of the wind ranges roughly from 50 to 200 m for a short green grass completely shading the ground.
	www.copernicus.org /EGU/hess/1/2/257.htm?FrameEngine=false (342 words)

	penman_monteith_11 (Site not responding. Last check: 2007-10-25)
		The enhanced physical basis and considerable flexibility of the combination models (such as Penman's) have resulted in their extensive use in the calculation of both free surface water evaporation and potential evapotranspiration.
		An advanced combination model which is gaining wide acceptance is the Penman-Monteith equation.
		Equation 2-53 can be conveniently expressed in Penman form (Eq.
	ponce.sdsu.edu /penman_monteith_11/penman_monteith_11.html (375 words)

	[No title]
		Penman himself recognized the limitations of using daily data to estimate real-time ET and recommended that his equation using daily data be used to estimate average ET over periods of 10 days or longer (Penman, 1948).
		Hourly estimates of reference evapotranspiration (RET) are calculated as: (1) RET = W(Rn)+(1-W)(VPD)(FU2) where Rn is the net radiation in equivalent mm of evaporation, W is a dimensionless weighing function, VPD is the vapor pressure deficit in kilopascals (KPa), and FU2 is an empirical wind function in mm of evaporation per KPa.
		Vapor pressure deficit is calculated as: (6) VPD = Es-E where Es is the saturation vapor pressure at the hourly average air temperature and E is the vapor pressure in kilopascals.
	ag.arizona.edu /azmet/data/Documentation/et.txt (1291 words)

	Priestley-Taylor Equation
		The adequacy of the assumptions made in the Priestley-Taylor equation has been validated by a review of 30 water balance studies in which it was commonly found that, in vegetated areas with no water deficit or very small deficits, approximately 95% of the annual evaporative demand was supplied by radiation (Stagnitti et al., 1989).
		The satisfactory performance of the equation is probably because the incoming solar radiation has some influence on both the physiological and the meteorological controls of evapotranspiration.
		Estimates of PET using the Priestley-Taylor equation have been adjusted as a function of the difference in albedo at the site where measurements of radiation have been made (albe), and the land classes with differing albedo (alb).
	www.civil.uwaterloo.ca /watflood/Manual/02_03_1.htm (626 words)

	5. 15 - pts. For Cairo, Egypt, in July, average net radiation is 185 W/m2, air temperature 28.5 ºC, relative ... (Site not responding. Last check: 2007-10-25)
		Therefore, in this limit, Penman equation yields a lower limit to the evaporation rate from moist surfaces, known as the equilibrium evaporation rate, and given by,
		However, equilibrium conditions are encountered only rarely, as air in the boundary layer is continually responding to large-scale weather patterns which tend to maintain a vapor deficit even over the oceans.
		In order to do so, two resistance parameters must be defined, one characterizing the transfer between the vapor saturated stomatal cavities and the surface of the leaf, and another characterizing the vapor transfer between the leaf surface and the ambient air within the dynamic sublayer.
	www.engr.colostate.edu /~ramirez/ce_old/classes/ce520_ramirez/ET_Equations/EvapotranspirationEquations.htm (1197 words)

	Chapter 4 - Determination of ETo
		The FAO Penman-Monteith equation determines the evapotranspiration from the hypothetical grass reference surface and provides a standard to which evapotranspiration in different periods of the year or in other regions can be compared and to which the evapotranspiration from other crops can be related.
		When applying the FAO Penman-Monteith equation on an hourly or shorter time scale, the equation and some of the procedures for calculating meteorological data should be adjusted for the smaller time step.
		Equations 45 and 46 can be used to derive G for the hourly periods.
	www.fao.org /docrep/X0490E/x0490e08.htm (2873 words)

	4 WEATHER
		Penman (1948) was the first to describe evapotranspiration in physical mathematical terms.
		The resulting equations are used to calculate the potential evaporation rates from a water surface, from bare soil surfaces and the potential evapotranspiration rate from a crop canopy.
		The temperature related weighing factor W in equation 4.1 is defined as (Frère and Popov, 1979; Penman, 1948, 1956).
	www.treemail.nl /download/treebook7/weather/chapt4.htm (5050 words)

	Crop evapotranspiration (BY M.I.T) (Site not responding. Last check: 2007-10-25)
		By defining the reference crop as a hypothetical crop with an assumed height of 0.12 m having a surface resistance of 70 s m-1 and an albedo of 0.23, closely resembling the evaporation of an extension surface of green grass of uniform height, actively growing and adequately watered, the FAO Penman-Monteith method was developed.
		It is important, when comparing the FAO Penman-Monteith equation to ETo measurements, that the full Penman-Monteith equation (Equation 3) and associated equations for ra and rs (Equations 4 and 5) be used to enable accounting for variation in ET due to variation in height of the grass measured.
		Differences between ETo values obtained with the FAO Penman-Monteith equation with, on the one hand, a limited data set and, on the other hand, a full data set, are expected to be smaller than or of similar magnitude to the differences resulting from the use of an alternative ETo equation.
	hydrotechnic.150m.com /crop_water.html (7520 words)

	Chapter 2 - FAO Penman-Monteith equation
		In 1948, Penman combined the energy balance with the mass transfer method and derived an equation to compute the evaporation from an open water surface from standard climatological records of sunshine, temperature, humidity and wind speed.
		The equation is restricted for neutral stability conditions, i.e., where temperature, atmospheric pressure, and wind velocity distributions follow nearly adiabatic conditions (no heat exchange).
		(Equations 4 and 5) be used to enable accounting for variation in ET due to variation in height of the grass measured.
	www.fao.org /docrep/x0490e/x0490e06.htm (3538 words)

	CIMIS - [ Equations ]
		The CIMIS Penman equation employs the modified Penman equation (Pruitt and Doorenbos.
		ETo estimated using the PM equation is referred to as the Penman-Monteith ETo or simply PM ETo.
		The hourly PM equation that CIMIS uses to estimate hourly PM ETo is the Food and Agricultural Organization's version that is described in Irrigation and Drainage Paper No. 56 (Allen, R.K., L.S. Pereira, D. Raes, and M. Smith.
	wwwcimis.water.ca.gov /cimis/infoEtoEquation.jsp (367 words)

	ARS \| Publication request: The Penman-Monteith Method
		This presentation discussed the fundamentals of the Penman equation and then the three main forms of the Penman-Monteith equation now in use in engineering and legal cases.
		Technical Abstract: The Penman equation was derived in 1948 from a combination of the energy balance and an aerodynamic equation.
		The empirical Penman equation from Idaho matched the measured evapotranspiration (ET) data the closest, but its correlation through regression revealed a high bias and low correlation.
	www.ars.usda.gov /research/publications/publications.htm?SEQ_NO_115=163834 (354 words)

	J. Cory Pettijohn
		Bouchet’s CR states that at a given surface moisture condition (MA), changes in ETa are reflected in changes in potential evapotranspiration (ETp) such that ETa + ETp = 2ET0, where ET0 is an assumed equilibrium condition at which ETa = ETp = ET0 given sufficiently large MA.
		I have utilized the FIFE dataset to demonstrate how the absence of a maximum, unstressed canopy conductance (gc,max) in a Penman equation with stability-corrected atmospheric conductance results in incomplete convergence between ETp and ETa near equilibrium.
		Inclusion of gc,max (replacing the Penman equation with an unstressed Penman - Monteith equation), significantly improves both CR convergence and symmetry, resulting in more precise ETa estimates than using Penman’s empirical wind function.
	people.bu.edu /geocory/BouchetMorton1.html (327 words)

	CIMIS - [ PM Equation ]
		The hourly Penman-Monteith equation for estimating reference evapotranspiration used on the CIMIS computer is a version described in the Food and Agricultural Organization's Irrigation and Drainage Paper No. 56 (Allen, R.K., L.S. Pereira, D. Raes, and M. Smith.
		However, bulk surface resistance is adapted from the ASCE Task Committee on Standardization of Reference Evapotranspiraton (2000).
		Two reference evapotranspiration equations are employed, one for a grass reference and the other for alfalfa.
	wwwcimis.water.ca.gov /cimis/infoEtoPmEquation.jsp (495 words)

	FERG Projects. Remi.
		Evapotranspiration is important as a term in the hydrological cycle, eg in soil water and ground water balances and in salinisation.
		There are a number of equations which give an approximate value of evapotranspiration and the most commonly used equation is the Penman-Monteith equation.
		Field values for the water balance equation were collected at small forested peatland catchments in Connemara (Cloosh valley).
	www.ucd.ie /ferg/Research/Projects/Remi.html (163 words)

	USGS--WRIA 1 Watershed Management Project--Estimating Evapotranspiration from Croplands
		The FAO-24 Penman technique (Doorenbos and Pruitt, 1977) was developed after Penman's (1948) combination energy-balance and aerodynamic equation.
		Both of these Penman-type equations employ the environmental variables of net radiation, soil heat flux, air temperature and water vapor pressure, and wind speed that are typically measured at a height of about 6 feet above the reference crop.
		Simple Et models, such as equation (1), are much less data-, labor- and equipment-intensive to apply than are Et measurement techniques.
	wa.water.usgs.gov /projects/wria01/data/et_narr.htm (1721 words)

	[No title] (Site not responding. Last check: 2007-10-25)
		In the investigated period (July to October 1997) Penman- Monteith reference evapotranspiration is 73% of Class A pan evaporation.
		Because of the large influence of temperature in the thermodynamically process of evaporation the results are improved when the latent heat,the density of air, the psychometric constant and the gradient of the saturated vapour pressure curve were calculated as functions of temperature.
		The equation can then be written as EMBED Equation.2 (5) The aerodynamic resistance ra in [s/m] by Feddes et al.
	www.ucc.ie /ucc/depts/civil/r_fell/Corinna/WindPowerConference/paperA4.doc (3490 words)

	Analytical Estimation of Modified Penman Equation Parameters (Site not responding. Last check: 2007-10-25)
		The mathematical expression of the modified Penman equation requires values for the adjustment factor C, the saturation vapor pressure and its slope with respect to air temperature, the extraterrestrial radiation, and the maximum sunshine duration, among others.
		Various research works found in the literature refer to the analytical evaluation of these parameters, but the need to more accurately calculate them is essential since errors introduced in evapotranspiration estimates are sometimes quite significant.
		In this paper, mathematical expressions that describe the parameters used for the calculation of the Penman reference crop evapotranspiration are derived through a nonlinear regression procedure.
	www.pubs.asce.org /WWWdisplay.cgi?9703363 (172 words)

	[No title]
		The equation that has proven to be the most effective in calculating reference ET is the ASCE Penman Monteith equation for cool season grass at 12 cm.
		The 1982 Kimberly Penman equation for alfalfa has likewise proven to be effective.
		Since either choice is a reference, the end user should modify the reference ET to match the needs of the particular crop and situation.
	www.coloradoet.org /whatiset.html (550 words)

	NAME__________________
		Remember to set up the equations completely before any calculations; most of the points will be based on your set-up.
		Derive your equations symbolically first (with variables only), and only then put in values to do your calculation.
		The equation for SA/V for a cylinder is
	trc.ucdavis.edu /rainbow/A13302T2ssol.htm (1074 words)

	Relative contribution of energy and aerodynamic components in Penman's equation at a semi arid tropical location. (Site not responding. Last check: 2007-10-25)
		Relative contribution of energy and aerodynamic components in Penman's equation at a semi arid tropical location.
		This study has shown that the relative contribution between energy and aerodynamic terms in Penman's formula on potential evaporation exists in the ratio of Delta : gamma which needs to be changed to Delta :6.14 gamma for the semi arid tropical location of Patancheru, Medak, Andhra Pradesh, India.
		With this modification the correlation coefficients between observed and estimated pan evaporation have changed from 0.46-0.66 to 0.94-0.99 during the test years of 1985-2002.
	trophort.com /information/data/B01/S04/SRI04REL1720823.html (173 words)

	ETo EVAPOTRANSPIRATION - REFERENCE CROP - AZMET
		The CIMIS Penman Equation was developed for use with hourly weather data.
		The Rno computed from Equations 2 and 3 is in units of W/m*m.
		Equation 1 requires net radiation in units of mm of equivalent water evaporation (Rn).
	ag.arizona.edu /azmet/et2.htm (882 words)

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