On Penman's equation for estimating regional evaporation

Abstract

SUMMARYThe form of Penman's evaporation equation most extensively applied in hydrometeorology is discussed. It is shown that this equation underemphasizes the importance of ventilation relative to radiation in maintaining regional evaporation. A generalized ventilation term is proposed and a modified equation for evaporation derived. This new equation is calibrated to give the same annual total for short vegetation as Penman's original version. It predicts both an enhancement of winter evaporation a t the expense of summer evaporation and a significant increase in annual total evaporation with vegetation size, especially in regions of frequent substantial rainfall. I~TRODUCTIONIn 1948 Howard L. Penman gave the first physically sound treatment of the difficult problem of estimating evaporation from natural surfaces. The equation which he developed links evaporation rate to the net flux of radiant energy at the surface and to the effective ventilation of the surface by air in motion over it. The so-called combination approach, in which both energy-balance and aerodynamic terms appear explicitly in a single relationship, is attractive for two reasons. The first is partly aesthetic. The relationship is both simple and realistic: it promotes an understanding of the physical process of evaporation from natural surfaces. The second reason, however, is entirely practical : the Penman equation requires meteorological information at one level only. Accordingly, it is far more readily applied than either the energy budget or the aerodynamic equations from which it was derived; so evaporation equations of the Penman or 'combination' type are amongst the most widely used in hydrology today.There exists, however, in the form of Penman's equation in current widespread use (see e.g. Grindley 1970), a certain incompatibility between the aerodynamic and energybalance terms. It therefore seems worth while to review the evolutionary steps which have led to this imbalance and, in the light of the current state of relevant micrometeorological knowledge, to suggest ways in which the Penman equation ought perhaps to be revised. THE BASIC EQUATIONPenman showed that the rate of evaporation from an open water surface could be expressed as where Q,, is the evaporation equivalent of the net flux of radiant energy to the surface, and the corresponding aerodynamic or ventilation term E, = (AQn, + y E , ) / ( A + y ) (mm day-') .(1) E, = O.26(es -e)( 1 + UjlOO) = E,, , say.The quantities e and es (mb) are the actual and saturation values of vapour pressure 2m above the surface and U is the corresponding wind run, in miles per day; y is the thermodynamic value of the psychrometric constant, equal to 0.66 mb K -' (near sea levelsee McCulloch 1965); and A = dee,/dT, the slope of the saturation-vapour-pressure versus 345

Ecosystem CO2/H2O fluxes are explained by hydraulically limited gas exchange during tree mortality from spruce bark beetles

“…All comparisons were Bonferroni corrected for multiple comparisons [Hochberg and Tamhane, 1987]. We checked the sensitivity of all analyses to the PenmanMonteith calculation using other definitions of aerodynamic resistance [Brutsaert, 1982;Campbell and Norman, 1998;Monteith and Unsworth, 2008;Thom and Oliver, 1977] as well as the definition of the growing season.…”

“…Data are jittered 2% of full scale in Figure 3b for display purposes. of β PET to the formulation of boundary layer resistance [Brutsaert, 1982;Kaimal and Finnigan, 1994;Massman et al, 1994;Monteith and Unsworth, 2008;Thom and Oliver, 1977]. This was done using a hierarchical Bayesian randomeffects model [Gelman et al, 2004;Rubin, 1981].…”

Investigating storage‐discharge relations in a lowland catchment using hydrograph fitting, recession analysis, and soil moisture data

“…Daily values of ET pot have been computed using data from the same meteorological station. Before 1988, the method of Thom and Oliver [1977] has been used and since 1989 the method of Makkink [1957]. For our approach, daily sums of ET pot have been disaggregated to hourly sums by multiplication with the relative contribution of hourly global radiation sums to the daily global radiation sums.…”

How significant is the usual assumption of neutral stability in evapotranspiration estimating models?

“…The aerodynamic resistance for latent or sensible heat transfer is affected by the stability conditions and may be expressed as (Thom & Oliver, 1977): Meteorol. Appl.…”