## 1. Introduction

[2] Evapotranspiration (*E*), is the largest term in the terrestrial water balance after precipitation. Additionally, its energetic equivalent, the latent heat flux (*λE*), plays an important role in the surface energy balance affecting terrestrial weather dynamics and vice versa. The importance of *E* in drylands, covering 45% of the Earth surface [*Asner et al*., 2003; *Schlesinger et al*., 1990], is critical since it accounts for 90–100% of the total annual precipitation [*Glenn et al*., 2007]. Therefore, an accurate regional estimation of *E* is crucial for many operational applications in drylands: irrigation planning, management of watersheds and aquifers, meteorological predictions, and detection of droughts and climate change.

[3] Remote sensing has been recognized as the most feasible technique for *E* estimation at regional scales with a reasonable degree of accuracy [*Kustas and Norman*, 1999; *Mu et al*., 2011]. Several methods have been developed for estimating regional *E* in the last decades. Many of them are based on the indirect estimation of *E* as a residual of the surface energy balance equation (SEB) using direct estimates of the sensible heat flux (*H*) derived from remotely sensed surface temperatures [*Glenn et al*., 2007; *Kalma et al*., 2008]. However, residual estimation of *E* in Mediterranean drylands remains problematic due to the reduced magnitude of *λE* in conditions where *H* is the dominant flux [*Morillas et al*., 2013]. Reduced inaccuracies affecting estimates of *Rn* and *H* derived from surface temperature measurements (∼10 and ∼30%, respectively) strongly affected the residually estimated values of *λE* (∼90% of error) in such conditions [*Morillas et al*., 2013]. This suggests that direct estimation of *E* might be more advisable in Mediterranean drylands.

[4] *Cleugh et al*. [2007] presented a method for direct estimation of *E* based on regional application of the Penman-Monteith (PM) equation [*Monteith*, 1964] using leaf area index (*LAI*) from MODIS (*Moderate Resolution Imaging Spectrometer*) and gridded meteorological data. This work stimulated a number of later studies [*Leuning et al*., 2008; *Mu et al*., 2007, 2011; *Zhang et al*., 2010, 2008] that have demonstrated the potential of the PM equation as a robust and biophysically based framework for *E* direct estimation using remote-sensing inputs [*Leuning et al*., 2008].

[5] The key parameter of the PM equation is the surface conductance (*G _{s}*), the inverse of the resistance of the soil-canopy system to lose water. A simple linear relationship between

*G*and

_{s}*LAI*was initially proposed by

*Cleugh et al*. [2007] to estimate

*E*at two field sites in Australia.

*Mu et al*. [2007, 2011] took one step forward with separate estimations for the two major components of

*E*: canopy transpiration (

*E*) and soil evaporation (

_{c}*E*), both controlled by different biotic and physical processes in sparse vegetated areas [

_{s}*Hu et al*., 2009].

*Mu et al*. [2007, 2011] included a formulation for

*E*considering the effects of vapor pressure deficit (

_{c}*D*) and air temperature (

_{a}*T*) on canopy conductance (

_{a}*G*) but assumed constant parameters for each vegetation type. Based on these studies,

_{c}*Leuning et al*. [2008] developed a less empirical formulation for

*G*to apply the PM equation regionally. This new formulation also considers both

_{s}*E*and

_{c}*E*. For

_{s}*G*, a more biophysical algorithm based on radiation absorption and

_{c}*D*was proposed by

_{a}*Leuning et al*. [2008] based on

*Kelliher et al*. [1995]. In this case,

*E*is estimated as a constant fraction,

_{s}*f*, of soil equilibrium or potential evaporation [

*Priestley and Taylor*, 1972] defined as the evaporation occurring under given meteorological conditions from a continuously saturated soil surface [

*Donohue et al*., 2010;

*Thornthwaite*, 1948]. Application of the

*Penman-Monteith-Leuning*, PML model, as it was named by

*Zhang et al*. [2010], requires commonly available meteorological data (more details in section 2),

*LAI*data from MODIS or other remote-sensing platforms and two main parameters, considered by

*Leuning et al*. [2008] to be constants:

*g*, maximum stomatal conductance of leaves at the top of the canopy and

_{sx}*f*, representing the ratio of soil evaporation to the equilibrium rate. The potential of the PML for global estimates of

*E*is promising as shown by accurate estimates (systematic root-mean-square error of 0.27 mm day

^{−1}) found in 15 Fluxnet sites located across a wide range of climatic conditions, from wetlands to woody savannas [

*Leuning et al*., 2008]. Nonetheless, the latter model has not been tested in Mediterranean drylands characterized by strongly reduced magnitudes of

*E*(mean annual

*E*values ranging 0.5 mm day

^{−1}) resulting from the typical asynchrony of energy and water availability in these environments [

*Serrano-Ortiz et al*., 2007].

[6] In drylands, where water availability is the main controlling factor of biological and physical processes [*Noy-Meir*, 1973], evaporation from soil can exceed 80% of total *E* [*Mu et al*., 2007]. Soil water availability, the main factor controlling *E _{s}* in water-limited areas [

*McVicar et al*., 2012]

*is highly variable in these ecosystems and, therefore, assuming*

_{,}*f*as constant, as the original PML model of

*Leuning et al*. [2008] did, is inadequate.

*Leuning et al*. [2008] acknowledged this limitation and recommended that remote-sensing or other techniques should be developed to treat

*f*as a variable instead of a parameter, especially for sparsely vegetated sites (

*LAI*< 3). Many authors have also claimed the necessity to increase the efforts to carefully quantify the

*E*contribution to total

_{s}*E*in low

*LAI*ecosystems as semiarid grasslands and shrublands [

*Hu et al*., 2009;

*Kurc and Small*, 2004]. Numerous

*E*models that include specific methods for

*E*estimation, from the simplest to the most complex formulations, exist [

_{s}*Allen et al*., 1998;

*Fisher et al*., 2008;

*Kite*, 2000;

*Mu et al*., 2007;

*Shuttleworth and Wallace*, 1985]. Special attention has been paid to this topic in the agronomy sector because from an agricultural point of view, soil evaporation is considered an unproductive use of water that requires quantification [

*Kite and Droogers*, 2000]. Thus, many efforts have been devoted to improve

*E*formulation in croplands [

_{s}*Kite*, 2000;

*Lagos et al*., 2009;

*Snyder et al*., 2000;

*Torres and Calera*, 2010;

*Ventura et al*., 2006]. The FAO 56 methodology [

*Allen et al*., 1998] is one of the most used methods in agricultural areas due to its capacity to estimate both

*E*and

_{s}*E*beyond standard conditions (well-watered conditions) and some subsequent refinements have been proposed [

_{c}*Snyder et al*., 2000;

*Torres and Calera*, 2010;

*Ventura et al*., 2006]. However, when applying this method, detailed local soil characteristics, such as depth of soil or soil texture, are needed for estimating

*E*. This limits the regional application of this model beyond agricultural areas where little detailed soil information is available. There are other types of models partitioning the total

_{s}*E*by considering a different number of layers or sources like the sparse-crop model of

*Shuttleworth and Wallace*[1985] or the model from

*Brenner and Incoll*[1997]. The layers are defined depending on the site-specific surface heterogeneity (i.e., canopy, bare soil, under plant soil, residue covered soil, etc.). These models have provided successful results in sparsely vegetated areas such as irrigated agricultural scenarios [

*Lagos et al*., 2009;

*Ortega-Farias et al*., 2007] and natural conditions [

*Domingo et al*., 1999;

*Hu et al*., 2009]. Yet, they require specific information regarding the vegetation physiology and the substrate. Furthermore, complex modeling of aerodynamic and surface resistances governing the flux from each layer is necessary, limiting its regional application. From another perspective, the distributed hydrological models also deal with

*E*estimation. These models consider all the water reservoirs, modeling runoff and infiltration processes in a basin scale using satellite data [

_{s}*Kite*, 2000;

*Kite and Droogers*, 2000] to offer

*E*estimates at macroscale basins. However, these models require the measurements of all the terms of the hydrological balance to be validated. Those measurements are not routinely available for many macroscale basins.

[7] From a more regionally operative point of view, several models designed for global *E* estimation have also successfully estimated *E _{s}* as a fraction,

*f*, of soil equilibrium evaporation, as the PML model proposed. That soil equilibrium evaporation rate has been estimated using the PM equation [

*Mu et al*., 2007, 2011] or the Priestley-Taylor equation [

*Fisher et al*., 2008;

*García et al*., 2013;

*Zhang et al*., 2010] but all these models considered

*f*as temporally variable.

*f*has been estimated as a function of

*D*, relative humidity and a locally calibrated parameter

_{a}*β*(which indicates the relative sensitivity of soil moisture to

*D*) every month or 8 days periods [

_{a}*Fisher et al*., 2008;

*Mu et al*., 2007, 2011].

*Garcia et al*. [2013] proved that such approach is very sensitive to

*β*parameter in a daily time basis and consequently proposed an alternative formulation for

*f*based on Apparent Thermal Inertia using surface temperature and albedo observations. Finally,

*Zhang et al*. [2010] used the ratio between precipitation and equilibrium evaporation rate as an indicator of soil water availability to obtain

*f*values over successive 8 days intervals.

[8] Because Mediterranean drylands are characterized by irregular precipitation which causes rapid increases in soil moisture during rain followed by extended drying periods, we considered it important to develop a specific formulation for *f* that models the soil drying process after precipitation. *Black et al*. [1969] and *Ritchie* [1972] presented a simple formulation to model the soil drying process as a function of the time (in days) following precipitation that we adapted for daily *f* estimation.

[9] The objective of this paper was to adapt and evaluate the PML model for estimating daily *E* in Mediterranean drylands where a more precise consideration of *E _{s}* is necessary. To achieve this goal, we tested three different approaches to estimate the temporal variation of

*f*: (i) using direct soil water content measurements; (ii) adapting

*Zhang*

*et al.*'s [2010] method for daily application; and (iii) including a simple model for modeling the soil drying after precipitation based on

*Black et al*. [1969] and

*Ritchie*[1972]. The PML model performance using the three

*f*approaches was evaluated by comparison with

*E*measurements obtained from eddy covariance systems at two functionally different Mediterranean drylands: (i) a littoral semiarid steppe and (ii) a shrubland montane site.