Mixture of Time Scales in Evaporation: Desorption and Self-Similarity of Energy Fluxes

at the soil surface (namely net radiation, sensible heat flux, and soil heat flux) (e.g., Brutsaert and Sugita, 1994; The time evolution of evaporation from a bare soil, over a 9-d Crago, 1996). Recently, Brutsaert and Chen (1996) properiod following irrigation, is described by a combination of daily and hourly drying patterns. From the second day, the daily evaporation posed a simple model to account for both daily and shows a second stage of drying that can be described as a desorptive hourly variations of evaporation over a grass prairie process (evaporation proportional to (t 2 to), where t is time in under intense drying (after the grass had wilted). This days and to is the day when the second stage starts). The short time model combines desorption at the daily timescale with (hourly) evaporation rate can be modeled on the basis of a type self-similarity at the hourly timescale to estimate the of self-similarity in the energy balance components. Combining the hourly variations of evaporation during the drying peevaporative flux behavior at the two time scales, desorption at the riod. The objective of the present paper is to test the daily timescale and self-similarity for the diurnal variations, a robust model proposed by Brutsaert and Chen (1996) for a description of evaporation for drying land surfaces is obtained. This bare soil during a 9-d drying period following irrigation. approach is tested using accurate measurements of the different comNote that this case differs from the case studied by ponents of the energy balance at the soil surface, obtained at 20-min intervals. The model accurately describes the time evolution of the Brutsaert and Chen (1996), mainly in the fact that the evaporative flux and could be used for the disaggregation of daily or components of the energy balance are known better weekly evaporation into hourly values. since the measurements are taken over a more homogeneous and flat land surface with well-defined wind direction and essentially cloud-free conditions. Effectively, T time evolution of evaporation has patterns of this is a more “controlled” experimental investigation variability over various time scales. The day-to-day than that of Brutsaert and Chen (1996). Due to the change in daily evaporation due to the loss of available different characteristics of the land surfaces, changes in water is modulated hour to hour by diurnal changes in the results obtained from the model can also be exavailable energy at the land surface. Several efforts have pected. In particular, the time shift to, from which evapobeen made to obtain simple, semiempirical models to ration can be described as a desorption phenomenon estimate evaporation fluxes at different time scales. A at a daily timescale, is significantly closer to the last review of these efforts is given in the Theory section. irrigation (or rainfall) event for bare soil. After a certain time, to, daily evaporation during drying periods (with no rain or irrigation supplied) can be modTHEORY eled as a desorptive process, that is, evaporation proportional to (t 2 to), where t is time in days (e.g., Gardner, Daily Timescale: Desorption 1959; Parlange et al., 1992, 1993, 1999). However, in The time evolution of evaporation appears to be dominated many applications, a daily time resolution is too coarse, by two different stages of drying. The first stage is characterand time steps of 30 min to 1 h are required. At the ized by an adequate water supply to the surface, and drying hourly time scale, there is evidence of similarity between is controlled by available energy at the surface (e.g., Katul the time variation of the latent heat flux and the time and Parlange, 1992; Parlange and Katul, 1992). In the second variation of the other components in the energy balance stage, after the upper level of the soil has dried to some extent, evaporation is controlled by the rate of water vapor supply from below, and it falls below the potential values of the F. Porté-Agel, St. Anthony Falls Lab., Dep. of Civil Engineering, first stage. The evaporation rate in the second stage can be Univ. of Minnesota, Minneapolis, MN; M.B. Parlange, Dep. of Geogdescribed as a desorption phenomenon, raphy and Environmental Eng., The Johns Hopkins Univ., Baltimore, MD; A.T. Cahill, Dep. of Civil Eng., Texas A&M, College Station, TX; A. Gruber, Dep. of Civil Engineering, TU-Graz, Graz, Austria. LEd 5 1 2 De(t 2 to) [1] Received 15 Sept. 1999. *Corresponding author (mbparlange@ jhu.edu). where LEd is the daily latent heat flux (in W m2) (d refers to daily totals), De is the desorptivity (in W m2 d), t is the Published in Agron. J. 92:832–836 (2000). PORTÉ-AGEL ET AL.: MIXTURE OF TIME SCALES IN EVAPORATION 833 time (daily timestep) and to is the time at which the second and Taylor (1972). See Eichinger et al. (1996) for a discussion on the experimentally observed value of the Priestley-Taystage starts (Gardner, 1959; Gardner and Hillel 1962). Several field studies (e.g., Jackson et al., 1976; Parlange et al., 1992, lor coefficient. The assumption of self-preservation works well when F is 1993) carried out over drying bare soil surfaces have demonstrated that, following irrigation, the first stage of drying nortaken as net radiation, Rn, available energy flux, (Rn 2 G) or (LE 1 H), incoming shortwave radiation S ↓ (Brutsaert and mally lasts on the order of a day or less. After this, a desorptive second stage of drying followed, described by Eq. [1]. Sugita, 1992), and LEe (so that R 5 a) (Crago, 1996). However, self-preservation appears to be less robust in the case of F 5 Brutsaert and Chen (1995) studied drying of a prairie grassland. As with bare soil evaporation, they also identified two H, for which R2 is the Bowen ratio b. Crago and Brutsaert (1996) showed that this is caused by the difference in error stages of drying, separated in this case by a transitional period. Initially, after rainfall or irrigation, evaporation from the soilpropagation between R and b. plant continuum occurred at the so-called potential rate (first stage). As the soil surface dried out, there was a transitional Combining Desorption and Self-Preservation period in which the vegetation continued to extract water from Brutsaert and Chen (1996) proposed a parameterization soil layers below the surface. Note that this transitional period for the second stage of drying of a grass covered soil surface was mainly a consequence of the active vegetation and thus (after grass has wilted), based on the combination of the deit was longer than in the case of bare soil. Finally, a second sorptive behavior for the daily variation as described by Eq. [1] stage (comparable to the second stage in bare soils) starts and the self-preservation assumption to describe the diurnal when the vegetation wilts and the roots cease extracting water variation as given by Eq. [2]. from the soil. Then evaporation takes place only from the soil Combination of Eq. [1] with Eq. [2] and [3] yields a paramesurface and it can be described as a desorption phenomenon terization for the ‘instantaneous’ latent heat flux (over the ith at the daily timescale (Cahill and Parlange, 1998; Parlange et period of the day), al., 1998).