Estimation of the diurnal variation of potential evaporation from a wet bare soil surface

Parlange, M.B. and Katul, G.G., 1992. Estimation of the diurnal variation of potential evaporation from a wet bare soil surface. J. Hydrol., 132: 71-89. Potential evaporation from a wet bare soil field was measured with a large sensitive weighing lysimeter on a 20 min time step for 5 days at Davis, California. The diurnal evaporation rate modeled with the Penman-Brutsaert model for potential evaporation with atmospheric stability corrections resulted in the best description of the measured fluxes. The Priestley-Taylor model was accurate for short intervals except when conditions of minimal advection were exceeded during the day. It was noted that the Priestley-Taylor formulation with ~t = 1.26 performs best under unstable atmospheric conditions. During stable conditions, the value of~ = 1.26 underpredicts the measured potential evaporation. The advection-aridity model for actual evaporation based on the Bouchet complementary relationship was studied. Strong advection explains the tendency found in other experimental studies to underpredict daily potential evaporation. A methodology to account for the excess advection is discussed in the complementary model, and the flux predictions were equivalent to the Penman-Brutsaert formulation for wet surfaces. I N T R O D U C T I O N A number of recent hydrologic studies have compared and evaluated different models for prediction of daily evaporation for applications in hydrologic modeling (e.g. Ali and Mawdsley, 1987; Doyle, 1990; Granger and Gray, 1990; Le Meur and Lu, 1990; Nullet and Giambelluca, 1990). These investigations are important in establishing the reliability of daily evaporation formulations. There is, however, a need for surface flux parameterization shorter time periods and when the diurnal variation of evaporation is needed. Shuttleworth (1988) noted that the time scales for hydrologic-climatic simulation are short by conventional hydrologic standards (i.e. 1 day). The atmosphere responds rapidly to the input of energy and water at the land surface and the characteristic atmospheric turbulent time scales range from 10 to 45 min (Wyngaard, 1990; Parlange and Brutsaert, 1990). Sensitivity studies 0022-1694/91/$03.50 © 1991 Elsevier Science Publishers B.V. All r ights reserved 72 M.B. PARLANGE AND G.G. KATUL with general circulation models (GCMs) have demonstrated the strong interdependence between land surface processes and the atmosphere (see Rowntree and Bolton, 1983; Mintz, 1984). As a result, climate modelers now use short-duration evaporation models which depend on more detailed descriptions of the surface processes (e.g. Dickinson et al., 1986; Sellers and Dorman, 1987). The evaporation component in the GCMs has been demonstrated to play a controlling role in the likelihood of droughts (Rind et al., 1990), the increased vigor of the hydrologic cycle and the diurnal range of surface temperatures over deserts (Warrilow and Buckeley, 1989). Evaporation models for short durations are necessary also for more precise hydrologic investigations of surface hydrology and groundwater recharge (Abramopoulos et al., 1988). Evaporation is second in magnitude to precipitation in the hydrologic cycle, and in some regions more than 70% of the precipitation is evaporated (Brutsaert, 1982, 1986; Eagleson, 1986; Kustas, 1990). Water transport in soils is also strongly dependent on the diurnal variation of evaporation. Quantifying evaporation from bare soil is critical for water resources development in arid regions and for bare or fallow agricultural lands (Soares et al., 1988; Wallace et al., 1990; Le Meur and Lu, 1990). Le Meur and Lu (1990) commented that a typical characteristic of arid regions is that potential evaporation is extremely high and available water is limited, emphasizing the need for accurate and robust potential evaporation models. The purpose of this study is to identify the capabilities of three models to describe the diurnal variation of potential evaporation over bare soils. The models studied are the Penman-Brutsaert potential evaporation model (Katul and Parlange, 1991), the Priestley and Taylor (1972) potential evaporation model, and the advection-aridity actual evaporation model (Brutsaert and Stricker, 1979) based on the Bouchet (1963) complementary relationship. These models require atmospheric measurements at only one level and no calibration of surface properties. They are compared with potential evaporation measurements on a 20 min time step, by means of a large weighing lysimeter (Pruitt and Angus, 1960) with wet bare soil, for 5 days in 1990 at Davis, California. MODEL B A C K G R O U N D The Penman-Bru t saer t model (Ep) The Penman (1948) potential evaporation equation is Ep = m ( R n -G) "~(1 W ) E A (1) where Ep is the potential evaporation, W = A/(A + 7) a dimensionless VARIATION IN POTENTIAL EVAPORATION FROM A SOIL SURFACE 73 weighing function, A the slope of the saturation vapor pressure-temperature curve, 7 the psychrometric constant and EA is the drying power of the air. The first term in the Penman equation is referred to as the equilibrium evaporation (Slatyer and McIlroy, 1961; Brutsaert, 1982). E A was presented by Penman as a bulk transfer function for daily or longer intervals expressed as a linear function of the mean horizontal wind speed. For diurnal evaporation estimation, the effect of atmospheric stability is important in the formulation of EA (Stricker and Brutsaert, 1978; Brutsaert, 1982; Mahrt and Ek, 1984). On the basis of Monin and Obukhov (1954) similarity theory, Brutsaert (1982) suggested that EA = k u . p ( q * q , ) [ l n ( Z d ° ~ \ Zov / $ v ( ~ ~ ) ] ' (2) where k -0.4 is Von Kfirmfin's constant, u. = (To~p) ~/2 is the friction velocity, z0 is the surface shear stress, p is the density of the air, do is the displacement height, z is the height of measurement above the surface, Z0v is the vapor roughness height, and qa and q* are the specific humidity of the air and the saturation specific humidity at air temperature, respectively. The similarity stability correction function of Monin and Obukhov (1954), $,, depends on y -(z do) /L where L is the Obukhov length, defined by 3 L = u. (3) kg[Hv/(pCp T a )] and Hv = (H + 0.61 T a Cp E) is the specific flux of virtual sensible heat, Cp the specific heat at constant pressure, T, the air temperature, E the actual evaporation rate, and H the specific flux of sensible heat. The Businger-Dyer stability functions (Dyer, 1974; Businger, 1988) can be described by Ov = 21n(1 +x2.) 2 ; (y < 0) (4) = 5[(zo/L ) y]; (0 < y ~< 1) (5) ~0~ = 5 1 n (Z d°~; (1 < y ) (6) \ , / Z 0 where x = (1 16y) TM. Equation (4) applies to unstable conditions and eqns. (5) and (6) to stable conditions. The friction velocity is obtained from the Monin-Obukhov model for the mean horizontal wind speed, 74 M.B. PARLANGE AND G.G. KATUL where V is the mean horizontal wind speed, z 0 is the surface roughness, and ~/m is the momentum stability correction function. For stable conditions the momentum correction functions are assumed to be equal to the vapor correction functions, and for unstable conditions l n [ # + x)2(1 + x2)~ q,m = + x0) 2 (1 + ~-0)_] 2 arctan x + 2 arctan x0 (8) where x0 = [1 16zo/L] 1/4. For a bluff-rough surface (e.g. bare soil) the scalar roughness (Z0v) may be estimated by z0v = 7.4z 0 exp [-2.25(z~/+ 4)] (9) where z0+ = (u, zo)/v is the roughness Reynolds number, and v is the kinematic viscosity (Brutsaert, 1975; Katul and Parlange, 1991). The evaporation is determined with an iteration procedure in the context of the one-dimensional surface energy budget, Ro O = Ep + /4 (10) where Rn is the net radiation and G is the soil heat flux. The system is initiated by assuming neutral stability conditions 0Pv : ~0m ---0) to determine u , , EA, and Ep. The initial value of Ep is used to obtain H by means of the energy balance and these initial values of Ep, u, and H provide a first estimate of L. The stability correction functions are then included through successive iterations until convergence of Ep is achieved. Priestley-Taylor Model (Eer) Priestley and Taylor (1972) obtained a simple model of the total input of water vapor from a large wet area. They found that under conditions of minimal advection Ep can be described by a constant proportion of the equilibrium evaporation, A EpT = ~ ~ (R, G) (11) where EpT is the Priestley-Taylor potential evaporation flux and ~ is the constant of proportionality. In the context of their work, Priestley and Taylor (1972) concluded that the eddy conductivity of heat (Kh) and the eddy diffusivity of vapor (Kv) tend to the eddy viscosity (K) in the atmospheric surface layer. Therefore, assuming similarity with Kh = Kv = K, both the specific humidity q and temperature T satisfy the same one-dimensional diffusion equation ~q,T ~ ( ~ q , ~ Ot ~ z \ K Oz ] (12) VARIATION IN POTENTIAL EVAPORATION FROM A SOIL SURFACE 75 For saturated surfaces, Priestley and Taylor proposed a variable which could satisfy (12), of the form (Oqs' A = q q~(Tm) \?TJr=:r,,, ( T Tm) (13) where Tm is some constant temperature between T~ and T, and qs is the specific humidity at the saturated surface. For A = 0, the solution yields the equilibrium evaporation E~q with Eeq A = ( 1 4 ) Heq + Eeq A + 7 where Heq is the sensible heat flux at equilibrium conditions. Equation (14) is not the most general solution to eqn. (12) but only a particular solution resulting from the case A = 0. Priestley and Taylor studied how much this solution explained the variation of the actual surface fluxes and proposed a modification of the form EpT A ( 1 5 ) HpT + EpT A + ~' where Hpx is the sensible heat flux obtained from the energy budget with a Priestley-Taylor defined evaporative flux. As the proposed solution in eqn. (15) must satisfy the boundary condition K?A/,~z = 0, ~ must be a constant independent of z /L . Priestley and Taylor (1972) established that ~ varies from unity to ( l /W) and that, experimentally, ~ = 1.26 for wet land surfaces and free water bodies. That ~ is about 1.26 shows that the advection-free conditions leading to an equilibrium state (Slatyer and McIlroy, 1961) are extemely unlikely to occur, and large-scale advection from extensive saturated surfaces accounts for roughly 20% of the evaporation rate (Brutsaert, 1982). This deviation from equilibrium conditions occurs because the turbulent atmosphere is continually responding to large-scale weather patterns that involve condensation and unsteady flow, which maintain a specific humidity deficit even above lakes and oceans (Brutsaert, 1982). Many studies have found that ~ is approximately equal to 1.26 for a variety of wet surfaces (e.g. Davies and Allen, 1973; Jury and Tanner, 1975; Stewart and Rouse, 1976, 1977; Doorenbos and Pruitt, 1977). The formulation has proven to be useful for humid sites with minimal advection (De Bruin and Holtslag, 1982; Stagnitti et al., 1989). Finally, the Priestley-Taylor method is simple to use, requiring little computational effort, and can yield accurate results if the assumptions of the model are met. 76 M.B. PARLANGE AND G.G. KATUE Advection-aridity model (E~a) The advection-aridity approach suggested by Brutsaert and Stricker (1979) for evaporation estimates for daily or longer periods relies on a complementary relationship between actual and potential evaporation, as proposed by Bouchet (1963) and developed by others including Morton (1969, 1975, 1983), Seguin (1975), and Fortin and Seguin (1975). This work was motivated by the need for a model to estimate actual rather than potential evaporation using only regularly measured quantities. The Bouchet complementary relation can be stated as Ep + E = 2E w (16) where Ep is the potential evaporation, E is the actual evaporation, and Ew is the evaporation from a wet environment. The potential evaporation is defined by Ep = Ew + ql (17) where ql is the energy that becomes available when E decreases below Ew, in the absence of excess advection (oasis effect). Brutsaert and Stricker suggested that the Priestley-Taylor model should be used to compute Ew (i.e. Ew = Epv) and the Penman equation to compute Ep (Nash, 1989). The advection-aridity model has proven useful on a daily or monthly basis when compared with field measurements (e.g. Brutsaert and Stricker, 1979; Ali and Mawdsley, 1987; Le Meur and Lu, 1990). When the surface is wet, Ali and Mawdsley (1987) noted that the advection-aridity equation can underestimate the evaporation rate.