Improving evapotranspiration estimates in Mediterranean drylands: The role of soil evaporation

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Improving evapotranspiration estimates in Mediterranean drylands: the role of

soil evaporation

Laura Morillas1, Ray Leuning

2, Luis Villagarcía

3, Mónica García

4,5, Penélope Serrano-

Ortiz1, Francisco Domingo

1

1Estación Experimental de Zonas Áridas, Consejo Superior de Investigaciones Científicas (CSIC), Ctra.

de Sacramento s/n La Cañada de San Urbano, 04120 Almería, Spain. ([email protected])

([email protected]) ([email protected])

2CSIRO Marine and Atmospheric Research, GPO Box 3023, Canberra ACT 2601, Australia.

([email protected])

3Departamento de Sistemas Físicos, Químicos y Naturales. Universidad Pablo de Olavide, Carretera de

Utrera km 1, 41013, Sevilla, Spain. ([email protected])

4Department of Geosciences and Natural Resource Management, University of Copenhagen, Øster

Voldgade 10, 1350 Copenhagen K, Denmark. ([email protected])

5International Research Institute for Climate & Society (IRI), The Earth Institute, Columbia University,

Palisades, New York 10964-8000, USA.

Corresponding author:

L. Morillas

E-mail address: [email protected]

Telephone: (+1) 505 277 8685 Fax: (+1) 505 277 0304

This article has been accepted for publication and undergone full peer review but has not beenthrough the copyediting, typesetting, pagination and proofreading process which may lead todifferences between this version and the Version of Record. Please cite this article as an‘Accepted Article’, doi: 10.1002/wrcr.20468

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ABSTRACT

An adaptation of a simple model for evapotranspiration (E) estimations in drylands

based on remotely sensed leaf area index and the Penman-Monteith equation (PML

model) [Leuning et al., 2008] is presented. Three methods for improving the

consideration of soil evaporation influence in total evapotranspiration estimates for

these ecosystems are proposed. The original PML model considered evaporation as a

constant fraction (f) of soil equilibrium evaporation. We propose an adaptation that

considers f as a variable primarily related to soil water availability. In order to estimate

daily f values, the first proposed method (fSWC) uses rescaled soil water content

measurements, the second (fZhang) uses the ratio of 16 days antecedent precipitation and

soil equilibrium evaporation, and the third (fdrying), includes a soil drying simulation

factor for periods after a rainfall event. E estimates were validated using E

measurements from eddy covariance systems located in two functionally-different

sparsely vegetated drylands sites: a littoral Mediterranean semi-arid steppe and a dry-

subhumid Mediterranean montane site. The method providing the best results in both

areas was fdrying (mean absolute error of 0.17 mm day-1

) which was capable of

reproducing the pulse-behavior characteristic of soil evaporation in drylands strongly

linked to water availability. This proposed model adaptation, fdrying, improved the PML

model performance in sparsely vegetated drylands where a more accurate consideration

of soil evaporation is necessary.

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1. INTRODUCTION

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 to 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.

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, 1996; 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.

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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., 2008, 2010] that have demonstrated the

potential of the PM equation as a robust, biophysically based framework for E direct

estimation using remote sensing inputs [Leuning et al., 2008].

The key parameter of the PM equation is the surface conductance (Gs), the inverse of

the resistance of the soil-canopy system to lose water. A simple linear relationship

between Gs and 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 (Ec) and soil

evaporation (Es), both controlled by different biotic and physical processes in sparse

vegetated areas [Hu et al., 2009]. Mu et al. [2007, 2011] included a formulation for Ec

considering the effects of vapor pressure deficit (Da) and air temperature (Ta) on canopy

conductance (Gc) but assumed constant parameters for each vegetation type. Based on

these studies, Leuning et al. [2008] developed a less empirical formulation for Gs to

apply the PM equation regionally. This new formulation also considers both Ec and Es.

For Gc a more biophysical algorithm based on radiation absorption and Da was proposed

by Leuning et.al. [2008] based on Kelliher et al. [1995]. In this case, Es is estimated as a

constant fraction, 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

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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: gsx, maximum stomatal

conductance of leaves at the top of the canopy and 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].

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 Es 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 Es contribution to

total E in low LAI ecosystems as semi-arid grasslands and schrublands [Hu et al., 2009;

Kurc and Small, 2004]. Numerous E models that include specific methods for Es

estimation, from the simplest to the most complex formulations, exist [Allen et al.,

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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 Es formulation in croplands [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 Es and Ec beyond standard conditions (well-watered

conditions) and some subsequent refinements have been proposed [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 Es. This limits the regional application of this model beyond agricultural

areas where little detailed soil information is available. There are other type of models

partitioning the total 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 Es estimation. These models consider all

the water reservoirs, modeling runoff and infiltration processes in a basin-scale using

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satellite data [Kite, 2000; Kite and Droogers, 2000] offering E estimates at macro-scale

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 macro-scale basins.

From a more regionally operative point of view, several models designed for global E

estimation have also successfully estimated Es 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 Da,

relative humidity and a locally calibrated parameter β ( which indicates the relative

sensitivity of soil moisture to Da) every month or 8-days periods [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.

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

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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.

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 Es 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’s et al. [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 semi-arid steppe; and (ii) a

shrubland montane site.

2. MODEL DESCRIPTION

2.1 Penman-Monteith-Leuning model (PML) description

Actual evapotranspiration (E) is the sum of canopy transpiration (Ec), soil evaporation

(Es) and evaporation of precipitation intercepted by canopy and litter (Ei) [D'odorico

and Porporato, 2006]. Despite the fact that Ei has been shown to account for up to 30%

of the annual rainfall in some arid communities [Dunkerley and Booth, 1999], the

magnitude of Ei is considered a small amount of the total water losses in areas with low

ecosystem LAI or short vegetation because of the reduced fraction cover of plants and

the lower aerodynamic conductance of these areas in comparison with forests [Mu et al.,

2007; Muzylo et al., 2009]. Moreover, in Mediterranean areas a reduced relative

magnitude of Ei can be expected because precipitation events are intense and they occur

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mainly in the lower available energy seasons (autumn and winter), both factors

decreasing the interception fraction [Domingo et al., 1998]. In this regard, Garcia et al.

[2013] reported no improvements on actual E estimation by considering Ei in two

natural semi-arid sites, one of them included in this work. Therefore, in the present

work only Ec and Es were considered for actual E estimation following the expression,

c sE E E (1)

The fluxes of latent heat associated with Ec and Es were written by Leuning et al. [2008]

as

p a

a

/

1 / 1

c a s

c

A ρc D G AE f

G G

(2)

where the first term is the PM equation written for the plant canopy and the second term

is the flux of latent heat from the soil expressed as a fraction of potential. The variables

Ac and As (W m-2

) are the energy absorbed by the canopy and soil respectively. Ga and

Gc (m s-1

) are the aerodynamic and canopy conductances, as defined below. ε (kPa K-1

)

is the slope (s) of the curve relating saturation water vapor pressure to air temperature

divided by the psychrometric constant (γ), ρ (kg m-3

) is air density, cp (J kg K-1

) is the

specific heat of air at constant pressure, and Da (kPa) is the vapor pressure deficit of the

air, computed as the difference between the saturation vapor pressure at air temperature,

esat, and the actual vapor pressure, e (Da = esat - e). The factor f in the second term of Eq.

2 modulates potential evaporation rate at the soil surface expressed by the Priestley-

Taylor equation, )1/(, sseq AE , by f = 0 when the soil is dry, to f = 1 when the soil

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is completely wet. In spite of the Priestley-Taylor formulation was designed to estimate

potential evaporation in energy-limited ecosystems [Priestley and Taylor, 1972], recent

works have demonstrated that accurate estimates of actual E can be determined in

water-limited conditions by downscaling Priestley-Taylor potential evapotranspiration

according to multiple stresses at daily time-scale [Fisher et al., 2008; Garcia et al.,

2013] as the PML model does through f.

To estimate partitioning of available energy between soil and canopy surfaces the Beer-

Lambert law has been applied by many authors even in sparse vegetated areas [Hu et

al., 2009; Leuning et al., 2008; Zhang et al., 2010]. Based on Beer-Lambert law soil

available energy can be estimated as As = Aτ and canopy available energy is Ac = A(1-τ),

where τ = exp(-kALAI) and kA is the extinction coefficient for total available energy A.

When eddy covariance data are used for validation, A = H +λE can be assumed in order

to ensure internal consistency in relation to eddy covariance closure error [Leuning et

al., 2008]. Kustas and Norman [1999] have however questioned the reliability of this

approach in sparse vegetation. Alternatively, they proposed a more complex method for

energy partitioning based on surface temperature and shortwave incoming radiation

retrievals that accounts for the different behavior of soil and canopy for the visible and

near infrared regions of spectrum. Preliminary analyses included in Appendix A showed

that mean absolute differences between daytime averages of Ac and As estimated by

those two energy partitioning approaches were minor (18 and 32 W m-2

for Ac and As

respectively) (Table A1) over 144 days in 2011 when infrared sensors were available to

measure surface temperature and shortwave incoming radiation. Because of these

reduced differences (Fig. A1) at daytime scale, the Beer-Lambert method was used to

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maintain the reduced number of PML model inputs. Of far greater importance is

correctly estimating f, as discussed below.

Aerodynamic conductance Ga is estimated using [Monteith and Unsworth, 1990]

ovromr

azdzzdz

ukG

/)(ln/)(ln

2

(3)

where k is Von Karman’s constant (0.40), u (m s-1

) is wind speed, d (m) is zero plane

displacement height, zom and zov, (m) are roughness lengths governing transfer of

momentum and water vapor and zr (m) is the reference height where u is measured. In

this version of Eq. 3 the influence of atmospheric stability conditions over Ga has been

neglected for two reasons: (i) in dry surfaces where Gc << Ga, E is relatively insensitive

to errors in Ga [Leuning et al., 2008; Zhang et al. 2008, 2010]; and (ii) in semi-arid

areas, where highly negative temperature gradients between surface and air temperature

are found, correction for atmospheric stability can cause more problems than it solves

for estimating Ga [Villagarcia et al., 2007]. The variables d, zom and zov were estimated

via the canopy height (h) in m, using the general relations given by Allen [1986]: d =

0.66h, zom = 0.123h and zov = 0.1.

Canopy conductance was estimated using Leuning, et al. [1995] formulation, based on

Kelliher et al. [1995], as follows,

5050

50

/1

1

)exp(ln

DDQLAIkQ

QQ

k

gG

aQh

h

Q

sxc (4)

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where kQ, is the extinction coefficient of visible radiation, gsx (m s-1

) is the maximum

conductance of the leaves at the top of the canopy, Qh (W m-2

) is the visible radiation

reaching the canopy surface that can be approximated as Qh = 0.8A [Leuning et al.,

2008] and Q50 (W m-2

) and D50 (kPa) are values of visible radiation flux and water

deficit respectively when the stomatal conductance is half of its maximum value. We

used Q50 = 30Wm-2

, D50 = 0.7kPa, kQ = kA = 0.6 following the sensitivity analysis

presented in Leuning et al. [2008].

The PML model (Eqs. 2 – 4) includes factors controlling canopy transpiration and soil

evaporation but accurate estimation of gsx and f is crucial for model success. Three

methods for estimating f, with increasing complexity, presented in the next section were

evaluated for improving PML performance in drylands.

2.2 Methods for f estimation

Evaporation from soil surfaces is mainly controlled by volumetric soil content in the top

soil layer [Anadranistakis et al., 2000; Farahani and Bausch, 1995] and has been

traditionally described occurring in three stages. An energy-limited stage (Stage 1)

when enough soil water is available to satisfy the potential evaporation rate (f=1), a

falling-rate stage (Stage 2) when soil is drying and water availability limits the soil

evaporation rate (0<f<1) and a third stage (Stage 3) when soil is dry and it can be

considered negligible (f=0) [Idso et al., 1974; Ventura et al., 2006]. We tested three

different methods to capture this dynamic of f.

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2.2.1 f as a function of soil water content data (fSWC)

We used measured values of volumetric soil water content measured at 4 cm depth

(θobs) rescaled between a minimum (θmin) and a maximum (θmax) threshold value to

estimate f following the expression,

= 1 when, θobs> θmax

fSWC = 0 when, θobs < θmin (5)

= obs min

max min

-

-

when θmin ≤ θobs ≤ θmax

θmin was experimentally estimated as the minimum value of the dry season and θmax as

the value of θ in the 24 h after a strong rainfall event, which can be considered as an

estimate of the field capacity [Garcia et al., 2013], using data measured during the

study period.

2.2.2 f as function of precipitation and equilibrium evaporation ratio (fZhang)

We tested the method proposed by Zhang et al. [2010] to estimate f using the ratio of

accumulated values of precipitation (P) and Eeq,s, both in mm day-1

, over N days. While

the original formulation of Zhang et al. [2010] was designed to estimate the averaged

value of f over successive 8-day intervals using accumulated values of P and Eeq,s in N =

32 days (covering 16 days prior and 16 days after the current day i ), we adapted this

method for daily estimates of f. After a sensitivity analysis, included in Appendix B,

here we set N = 16, between day i and fifteen preceding days (i-15), to estimate daily f

using measured values of P and Eeq,s and it is expressed as,

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1,min

15

,,

15

i

i

iseq

i

i

i

Zhang

E

P

f (6)

where Pi is the accumulated daily precipitation and Eeq,s,i is the daily soil equilibrium

evaporation rate for day i.

2.2.3 f as a function of soil drying after precipitation (fdrying)

Black et al. [1969] formulated the cumulative evaporation in terms of the square root of

time after precipitation considering the soil drying process after rain and Ritchie [1972]

used the same approach for modeling the Stage 2 of soil evaporation. Thus for daily f

estimation we proposed to add a similar formulation for the soil drying periods during

dry days in combination with the fZhang method (Eq. 7) used here to estimate f during the

effective precipitation days (Pi > Pmin = 0.5 mm day-1

). This is,

= 15

, ,

15

min , 1

i

i

i

i

eq s i

i

P

E

when Pi > Pmin

fdrying (7)

= fLP exp(-α Δt ) when Pi ≤ Pmin

where fLP is the f value for the last effective precipitation day, Δt is number of days

between this and the current day i and α (day-1

) is a parameter controlling the rate of soil

drying, higher α values reflecting higher soil drying speed. For simplicity α was

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considered a constant estimated by optimization, even though it is known that α is

related to air temperature, wind speed, vapor pressure deficit and soil hydraulic

properties [Ritchie, 1972].

3. MATERIAL AND METHODS

3.1 Validation field sites and measurements

The PML model was evaluated at two experimental sites located in southeast Spain

characterized by Mediterranean climate, sparse vegetation (LAI < 1) and winter-rainfall

(see Table 1). Both sites are water-limited areas, following the classification proposed

by McVicar et al. [2012], with dryness index [Budyko, 1974] of 2.8 and 2.3,

respectively, during the study period. These are stronger aridity conditions than where

the PML model has been previously tested [Leuning et al., 2008; Zhang et al., 2010].

<Insert Table 1>

Water vapor fluxes were measured at each site using eddy covariance (EC) systems

consisting of a three axis sonic anemometer (CSAT3, Campbell Scientific Inc., USA)

for wind speed and sonic temperature measurement and an open-path infrared gas

analyzer (Li-Cor 7500, Campbell Scientific Inc., USA) for variations in H2O density.

EC sensors were located above horizontally uniform vegetation at 3.5 m at Balsa Blanca

and at 2.5 m at Llano de los Juanes (zr = 3.5 and zr = 2.5 respectively). Data were

sampled at 10 Hz and fluxes were calculated and recorded every 30 min. Corrections for

density perturbations [Webb et al., 1980] and coordinate rotation [Kowalski et al., 1997;

McMillen, 1988] were carried out in post-processing, as was the conversion to half-hour

means following Reynolds’ rules [Moncrieff et al., 1997]. The slope of the linear

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regressions between available energy (Rn - G) and the sum of the surface fluxes (H +

λE) yields a slope ~ 0.8 in Balsa Blanca and ~0.7 in Llano de los Juanes. This is

consistent with the ~20% of energy imbalance found in the European FLUXNET

stations [Franssen et al., 2010].

Complementary meteorological measurements were also made at each field site. An

NR-Lite radiometer (Kipp & Zonen, The Netherlands) measured net radiation over

representative surfaces at 1.9 m height at Balsa Blanca and 1.5 m at Llano de los Juanes.

Soil heat flux was calculated at both sites following the combination method [Fuchs,

1986; Massman, 1992], as the sum of averaged soil heat flux measured by two flux

plates (HFT-3; REBS) located at 0.08 m depth, plus heat stored in upper soil measured

by two thermocouples (TCAV; Campbell Scientific LTD) located at two depths 0.02 m

and 0.06 m. Air temperature and relative humidity were measured by

thermohygrometers located at 2.5 m height at Balsa Blanca field site and 1.5 m at Llano

de los Juanes (HMP45C, Campbell Scientific Ltd., USA). A 0.25 mm resolution

pluviometer (model ARG100 Campbell Scientific INC., USA) was used to measure

precipitation at Balsa Blanca and a 0.2 mm resolution pluviometer was used at Llano de

los Juanes (model 785, Davis Instruments Corp. Hayward, California, USA). Soil water

content was measured at both sites using water content reflectometers (model CS616,

Campbell Scientific INC., USA) located at 0.04 m depth with a reported accuracy by

the manufacturer of ±2.5% volumetric water content. Due to the high soil heterogeneity,

three randomly located sensors were averaged to obtain a representative SWC value at

Llano de los Juanes, while at Balsa Blanca one sensor located in bare soil was used. All

complementary measurements were recorded every 30 min using dataloggers (Campbell

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CR1000 and Campbell CR3000 dataloggers, Campbell Scientific Inc., USA) and

daytime ( from sunrise to sunset) averages were used for model running.

3.2 Remotely sensed data

LAI estimates were level 4 Moderate Resolution Imaging Spectrometers (MODIS)

composite products provided by the ORNL-DAAC (http://daac.ornl.gov): (i) MOD15A

(collection 5) from the Terra satellite; and (ii) MYD15A2 from the Aqua satellite, both

with a temporal resolution of 8 days. The averaged value of LAI reported from

MOD15A and MYD15A2 for the 3 km x 3 km area centered on each site EC tower was

computed. Filtering was performed according to MODIS quality assessment QA flags

to eliminate poor quality data (affecting 5 and 3 observations at Balsa Blanca site and

Llano de los Juanes respectively) which were replaced by the average of previous and

subsequent LAI values.

3.3 Model performance evaluation

Average daytime E measurements were used to validate daily estimates of E derived

from the PML model run using average daytime micrometeorological data [Cleugh et

al., 2007; Leuning et al., 2008; Zhang et al., 2010]. The measurement datasets were

divided into an optimization period, to estimate locally specific gsx and α values using

the rgenoud package for the R software environment [Mebane and Sekhon, 2009], and a

validation period, to validate PML model outputs at both field sites (see Table 2). The

optimization was performed to find the values of gsx and α that minimized the cost

function F for the total sample number, N (See N values in Table 2 and 4), that is:

N

EEF

N

i iobsiest

1 ,, (8)

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where Eest,i is estimated E for day i and Eobs,i is observed E for same day.

<Insert Table 2>

Standarized Major Axis Regression (SMA) type II [Warton et al., 2006] was used for

comparing daily measurements and model estimates of E during the validation period.

SMA regression attributes error in the regression line to both the X and Y variables, a

method which is recommended when the X variable is subject to measurement errors, as

is assumed for the EC system measurements used in this work. Slope, intercept and

coefficient of determination (R2) computed using SMA regression were reported in XY

plots. Mean absolute difference (MAD) [Willmott and Matsuura, 2005] are used for

quantitative evaluation of PML model results, while root mean square difference

(RMSD) are also presented for comparison with previous works. Systematic and

unsystematic components of RMSD [Willmott, 1982] are also reported. A low

systematic difference indicates model structure adequately captures the system

dynamics [Choler et al., 2010].

4. RESULTS

The two studied sites are Mediterranean drylands with clear functional differences (Fig.

1A and B). Both sites presented a very different temporal pattern in phenology (LAI)

with an early-spring maximum at Balsa Blanca and a late-spring maximum at Llano de

los Juanes. Balsa Blanca presented intermittent rainfall throughout the year causing a

more fluctuating SWC pattern than at Llano de los Juanes which had distinct wet and

dry seasons. These functional differences were also found in the temporal E pattern, that

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was more fluctuating at Balsa Blanca where E was more strongly linked to the SWC

(Fig. 1A and C), than at Llano de los Juanes where phenology was the main factor

controlling E (Fig. 1B and D).

<Insert Figure 1>

Optimized values of gsx were similar for both field sites under the three proposed

formulations for f (gsx ranging from 0.0067 to 0.0109 m s-1

) (Table 3). On the other

hand, α = 0.137 day-1

at Balsa Blanca was considerably lower than α = 0.478 day-1

at

Llano de los Juanes, which indicates the model considered a faster drying rate for Llano

de los Juanes than for Balsa Blanca. Experimental values of θmax and θmin for applying

fSWC were θmax = 0.20 m3

m-3

and θmin = 0.05 m3

m-3

at Balsa Blanca, and θmax = 0.35 m3

m-3

and θmin = 0.10 m3

m-3

at Llano de los Juanes.

<Insert Table 3>

Predictions of E obtained using the PML model with fdrying were superior to both fSWC

and fZhang, yielding the lowest values of MAE (0.17mm day-1

) and RMSE (0.22-0.24

mm day-1

) at both study sites (Table 3). The percentage systematic difference was low

using fdrying especially at Balsa Blanca site (18%), where fZhang also presented a low

percentage systematic difference (5%). However, percentages of systematic difference

remained higher at Llano de los Juanes using any of the three proposed methods for

estimate f (40-42%).

Page 20

20

Using fSWC the PML model resulted in strong overestimations of E following heavy

rainfall at both field sites (Fig. 1E and F). A similar tendency was observed running the

PML model using fZhang but not using fdrying that clearly reduced that tendency reaching a

closer agreement with observations. However, all three methods for estimating f

overestimated E when observed E was lower than 0.2 mm day-1

at Balsa Blanca, but

systematically underestimated E at the beginning of the dry season at Llano de los

Juanes mountain site coinciding with great part of the growing season (April to July of

2005). Reasons for this are discussed in the next Section.

Estimated values of daily E from the PML model are compared to observations at both

field sites in Fig. 2. Using fdrying in the PML model resulted in the best slope ( 0.98) and

intercept (0.01) for linear correlation versus observed E, though the coefficient of

determination (R2

= 0.47) using fdrying was slightly lower than with fSWC (R2

= 0.54) at

Balsa Blanca. Despite the better correlation achieved using fSWC, this method tended to

overestimate E values (Fig. 2A), a problem not found using fdrying (Fig. 2E). The highest

correlation at Llano de los Juanes was again obtained using fdrying (R2

= 0.59), whereas

using fSWC and fZhang produced two clusters of high and low predictions (Fig. 2B and D)

and hence poor coefficients of determination (R2 = 0.24 and R

2 = 0.31 respectively).

However, the tendency of the PML model with fdrying to underestimate E during the

growing season at this site (when E > 1.10 mm day-1

) reduced the linear agreement

resulting in a linear regression slope of 0.79 (Fig. 2F)

<Insert Figure 2>

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21

Additional analyses were performed to determine if the systematic underestimation of E

found at Llano de los Juanes during the growing season (Fig. 2F) using the three f

methods was caused by a too low gsx value reducing Ec. To evaluate if underestimates of

gsx were being obtained by including in the optimization dataset periods showing a very

different vegetation activity at this strongly seasonal site (the growing and the non-

growing season) (Fig. 1B), parameters optimizations were performed using specific

periods (Table 4).

<Insert Table 4>

Our results showed that estimates of model parameters (gsx and α) did not significantly

differ using different optimization periods (Table 4). Only optimized values of the gsx

parameter for the non-growing season using fSWC and fZhang were clearly lower. These

lower values of gsx generated a better fit of model output during the non-growing season

using fSWC and fZhang but strongly increased the underestimates of E for the growing

season (Fig. 4). Thus, improvement of model performance during the dry and growing

season of the validation period was not found using model parameters optimized

specifically for those conditions (Fig. 4B). This test also showed a low sensitivity of the

optimization method to the time period used especially using fdrying (Table 4).

<Insert Figure 4>

5. DISCUSSION

Important functional differences were observed between the two field sites, with an E

pattern more strongly linked to SWC at Balsa Blanca but better explained by phenology

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22

in Llano de los Juanes (Fig. 1A and B). These results can be understood considering the

vegetation composition and geomorphological characteristics of both field sites.

At Balsa Blanca, the vegetation is dominated by the perennial grass S. tenacissima

(57.2%) that is well-adapted to aridity and shows opportunistic growth patterns with

leaf conductance and photosynthetic rates largely dependent on water availability in the

upper soil layer [Haase et al., 1999; Pugnaire and Haase, 1996]. This explains the

observed link between E and SWC pattern here, where both Es and Ec are controlled by

water availability in the upper soil layer. In contrast, the vegetation at Llano de los

Juanes is co-dominated by perennial grasses, Festuca scariosa (Lag.) Hackel (19%),

and shrubs, Genista pumila ssp pumila (11.5%) and Hormatophylla spinosa (L). P.

Küpfer, (6,3%) [Serrano-Ortiz et al., 2007; Serrano-Ortiz et al., 2009]. At this montane

site, extraction of water by shrubs from deep cracks and fissures in the bedrock has been

previously detailed [Cantón et al., 2010] explaining the phenological control of E

during the dry period and the coincidence of the dry and growing seasons. These

functional considerations of the sites help to understand the performance of the three

proposed methods to improve E estimates by the PML model.

5.1 Using soil water content data to estimate soil evaporation (fSWC)

Despite the fact that the energy consumed by Es mainly depends on the moisture content

of the soil near the surface in water-limited areas [Leuning et al., 2008; McVicar et al.,

2012], the PML model using fSWC (Eq. 5) provided unsatisfactory estimates of E (Table

3). This method tended to systematically overestimate E at Balsa Blanca (Fig. 2A) and

presented a poor linear agreement with measured E at Llano de los Juanes (Fig. 2B). A

similar approach to fSWC was used by Garcia et al. [2013] to estimate Es at Balsa Blanca

and another woody savanna site but using a different approach to estimate daily Ec

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23

based on Fisher et al. [2008]. These authors found better E estimates using fSWC with R2

values ranging from 0.74 to 0.86. Our poorer results may be due to inaccuracies

affecting the experimental threshold values θmin and θmax. In the present study, these

values were estimated using data from the study period (Table 2), whereas Garcia et al.

[2013] used a more extended study period (6 years) to estimate θmin and θmax.

Nevertheless, as only estimates of total E were evaluated in both studies, it is difficult to

conclude that the disparity between both studies derives from better Es estimates, since

more accurate estimates of Ec obtained through their daily adapted version of Fisher et

al. [2008] model may also explain these differences. At the mountain site Llano de los

Juanes, different reasons may explain the poor performance of fSWC. E underestimates

found during the growing season using fSWC were a consequence of an underestimated

value of gsx (gsx=0.0076 m s-1

) found from optimization using fSWC. This gsx value was

lower than the one obtained using fZhang and fdrying (Table 3) resulting in stronger

underestimates of E during this period than the other two methods (Fig. 1F). As Fig. 3B

shows, a higher gsx value (gsx=0.0088 m s-1

) derived from optimization in the growing

season (Table 3) reduced the aforementioned underestimates during that period (Fig.

3B). In contrast, during the wet season (November to March 2006) using fSWC led to

overestimates of E (Fig. 1F) that we attributed to an effect of the high stoniness and

frequent rock outcrops (30-40% rock fragment content) found in this field site [Serrano-

Ortiz et al., 2007]. This high percentage of rock coverage reduces the effective soil

surface described by the SWC data and results in Es overestimations. Consequently, our

results suggest the necessity to adjust the fraction of transpiring soil surface in order to

use SWC measurements to estimate Es as a portion of the equilibrium rate in areas with

an important percentage of rocks.

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24

5.2 Using precipitation and equilibrium evaporation to estimate soil evaporation

(fZhang)

Use of fZhang in the PML model resulted in a strong overestimation of E during periods

following heavy or intermittent rain events (Fig. 1E and F). Thus, we found generally

low correlations with observations at both field sites (Fig. 2C and D). This occurred

because fZhang (Eq. 6) assumes that the effect of rain over the soil water availability is

limited to a time period of N days (N=16). As a result, after precipitation the model

predicts that f reaches high values remaining high for “N” days, after which an artificial

drop takes place or, when rainfall is heavy and intermittent, the model predicts f=1

during maintained periods of time. This is not an accurate representation of the real

SWC pattern, which actually increases during rain and decreases progressively after rain

events. Originally Zhang et al. [2010] used this approach to estimate f over 32-day

intervals for which a coarse resolution could be effective. They obtained an RMSD of

0.56 mm day-1

for a sparsely vegetated savanna site in Australia (Virginia Park) where

the mean annual E (1.20 mm day-1

) was higher than that of our field sites. When we

applied our proposed daily version of fZhang to our sites, we obtained an RMSD of 0.34-

0.31 mm day-1

. Since the mean annual was 0.49 mm day-1

at Balsa Blanca and 0.56 mm

day-1

at Llano de los Juanes (Table 3) this RMSD is relatively larger than the reported

by Zhang et al. [2010]. In other words, these results showed that the fZhang method did

not improve PML model performance in Mediterranean drylands. The increase of SWC

as a result of a rain event depends on the prior rain SWC level. Zhang et al. [2010] tried

to incorporate this concept using the ratio of accumulated values of P and Eeq,s during N

previous days for modeling f. However, this method is unable to record rapid decreases

of SWC following rain in Mediterranean drylands where a higher temporal resolution is

necessary to capture the daily variation of SWC.

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25

5.3 Modeling the soil drying process to estimate soil evaporation (fdrying)

Adoption of the fdrying method clearly improved PML model performance at both sites

(Table 3), outperforming the other two approaches (fSWC and fZhang) (Fig. 1E and F). E

estimated using fdrying did not show the strong overestimation obtained using fSWC or

fZhang after rainfall, showing a better capacity to describe the gradual drying of soil

following rainfall. This method uses the formulation based on Zhang et al. [2010] to

estimate the increment of SWC as result of each precipitation event but it included a

simple method to model the decrease of SWC during Stage 2 as a function of time after

the last precipitation (Eq. 7). Considering the difficulties associated with E-modeling in

Mediterranean drylands, where measured E rates are especially low, often not exceeding

the error range of methods for estimating E from remote sensing [Domingo et al., 2011],

using fdrying the PML model achieved reasonable agreement with EC-derived daily E

rates. This method showed an RMSD of 0.22-0.24 mm day-1

and R2 from 0.47 to 0.59

(Fig. 2E and F). This accuracy level is similar or slightly better than the results found by

Leuning et al. [2008] and Zhang et al. [2010] in the Australian woody savanna sites

Tonzi and Virginia Park. Fisher et al. [2008] found better correlation between estimates

and EC-derived monthly averages of λE (R2 ~0.8) at those two same Australian sites.

However, their model overpredicted λE during low λE periods [Fisher et al., 2008]

similarly to the overestimations that we found at Balsa Blanca site (when E was lower

than 0.2 mm day-1

) (Fig. 1E). Garcia et al. [2013] found R2 values of 0.58 and 0.82 at

two drylands (including Balsa Blanca site) using the same approach to estimate Ec than

Fisher et al. [2008] but including a different approach for f based on Apparent Thermal

Inertia derived from in situ surface temperature and albedo measurements. However,

their results deteriorated further than ours (R2=0.32) when remote sensed surface

temperature and albedo from SEVIRI (Spinning Enhanced Visible and Infared Imager)

Page 26

26

were used to estimate f at Balsa Blanca site. Improved MODIS global terrestrial E

algorithm combined with tower meteorological data found RMSD values of 0.67-0.91

mm day-1

and R2 values ranging from 0.24 to 0.78 in three woody savannas (including

Tonzi site) where observed E was 0.94-2.08 mm day-1

[Mu et al., 2011]. Eventhough, in

two shrubland sites, where observed E was 1.04 and 0.19 mm day-1

respectively, the

same model reached higher inaccuracies than ours, with RMSD values of 1.10 mm day-1

(R2=0.02) and 0.31 mm day

-1 (R

2=0.35). These previous results demonstrate that the

accuracy level found by the PML model using fdrying was similar or even outperformed

previous models to estimate E using remote sensing data in drylands where E modeling

is still a challenging task [Domingo et al., 2011].

Like fZhang, fdrying shares the advantage of only requiring widely-available precipitation

and equilibrium evaporation data, with the expense of a single additional parameter α.

With the use of fdrying the PML model was able to capture the varying controls on Es at

both field sites (Fig. 1E and F). Thus, the optimized value of the α parameter,

representing the speed at which soil reduces the capacity to evaporate water, was lower

at Balsa Blanca (α = 0.137 day-1

) than at Llano de los Juanes (α = 0.478 day-1

). This

implies that Es at Balsa Blanca has a longer period of influence on total E than at Llano

de los Juanes where the soil is assumed to dry more quickly. This is in agreement with

the fact that Llano de los Juanes is a karstic area characterized by infiltration occurring

in preferential flows through the abundant cracks, joints and fissures [Cantón et al.,

2010; Contreras, 2006].

Overall, the stronger phenological control over E, the reduction of effective evaporative

soil surface due to stoniness and rocky soil features and the importance of infiltration at

Page 27

27

Llano de los Juanes, contribute to Es having a less important role in total E dynamics

than at Balsa Blanca. This explains the higher systematically percentage differences

found at Llano de los Juanes (Table 3) where all three adapted model versions,

including fdrying, were less effective at capturing the system dynamics because they were

designed to improve Es, a less crucial factor at this site.

The systematic underestimation of E by the PML model at the beginning of the dry

season observed at Llano de los Juanes (Fig. 2D) using fdrying (and also with fZhang ) was

proven not to be a consequence of underestimates of Ec resulting from failed optimized

values of gsx (Fig. 3). In fact, tests optimizing model parameters using different

optimization periods showed consistency for gsx, especially using fdrying, the method less

sensitive to changes in the optimization period (Table 4). Therefore, underestimates of E

by the PML model using fdrying (and fZhang) at the beginning of the dry season were

explained instead by errors in Es caused by low f values. During this period, the effect of

precipitation from the preceding wet season (finishing 20 days before our validation

period) was not considered by fdrying (or fZhang) because these methods assume that the

effects of rain over SWC only persist during N days (N=16, in this case). In summary,

underestimates of E along the dry and growing seasons at our montane site showed the

limitation of fdrying, and fZhang to capture high soil water availability levels originated by

the cumulative effect of a long prior wet season.

6. CONCLUSION

The capacity of Penman-Monteith-Leuning model (PML model) to estimate daily

evaporation in sparsely-vegetated drylands is demonstrated through the development of

methods for temporal estimation of the soil evaporation parameter f. We advanced

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28

Leuning et al. [2008] who found that estimating soil evaporation parameter f as a local

time constant produced poor results in sparsely-vegetated areas (LAI < 2.5). Out of three

proposed methods, fdrying showed the best results for PML model adaptation at two

experimental sites and was able to capture the daily pattern of near surface soil moisture

content. This proposed method considers the soil water availability conditions previous

to rainfall to estimate the SWC increment derived from rain and explicitly models the

progressive soil drying process following precipitation. This way, the fdrying method

avoided the strong overestimates of E obtained with two other f estimation approaches,

fSWC and fZhang. Nevertheless, the fdrying method showed some limitations in its ability to

model the soil evaporation rate when this was influenced by high soil water availability

levels during the growing season from the cumulative effect of a long prior wet season

at Llano de los Juanes.

The use of time-invariant parameters for evaporation modeling is a delicate issue in

drylands and other extreme ecosystems where vegetation and soil are exposed to strong

fluctuations in environmental conditions. Where a simplifying compromise is required

in the design of operational and regionally applicable models, we showed here that

reasonable results can be obtained using temporally-constant estimates of gsx and α in

the PML model and the robustness of optimization period to estimate model parameters.

Appendix A

To evaluate the differences in available energy (A) partitioning between soil (As) and

canopy (Ac) using the Beer-Lambert law (BL) or the method proposed Kustas and

Norman [1999] specifically designed for sparse vegetation (K&N), daytime estimates of

As and Ac obtained following these two different methods were compared at Balsa

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29

Blanca during a 144 days (15 January to 8 June, 2011). During this time period one

Pyranometer (LPO2, Campbell Scientific, Inc., USA) and two broadband thermal

infrared thermometers (Apogee IRT-S, Campbell Scientific, Inc., USA) were available

at this site to measure incoming short-wave radiation and surface temperatures

necessary for K&N method application. Measurements of: (i) composite soil-vegetation

surface (TR); and (ii) pure bare soil surface (Ts) at the field site were obtained using

Apogee IRT-S, and canopy temperature (Tc) was derived from both applying the

nonlinear relation between TR,Ts and Tc based on vegetation cover fraction proposed by

Norman et al. [1995]. Further details can be found in Morillas et al. [2013].

To estimate As and Ac using the Beer-Lambert law, As BL and Ac BL were estimated as

follows

As BL= Aexp(-kALAI) (A.1)

Ac BL= A[1- exp(-kALAI)] (A.2)

where kA = 0.6 and A = H +λE using daytime measured averages of H and λE [Leuning

et al., 2008].

To estimate As and Ac using the method proposed Kustas and Norman [1999], As K&N

and Ac K&N where estimated following Eq. A.3 and A.4

As K&N =Rns-G (A.3)

Ac K&N =Rnc (A.4)

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30

where Rns and Rnc are daytime averaged estimates from Eq. A5 and A.6 and G is

daytime averaged soil heat flux measured (Section 3.1).

SLnRn ssss )1( (A.5)

SLnRn cscc )1)(1( (A.6)

where S (W m-2

) is the incoming shortwave radiation, τs is solar transmittance through

the canopy, αs is soil albedo, αc is the canopy albedo. Estimates of τs, αs and αc are

computed following the equations 15.4 to 15.11 in Campbell and Norman [1998] and

based on LAI, the reflectances and trasmittances of soil and a a single leaf, and the

proportion of diffuse irradiation, assuming that the canopy has a spherical leaf angle

distribution.

Lns and Lnc (W m-2

) are the net soil and canopy long-wave radiation, respectively,

estimated using the following expression:

scLskyLs LLLAIkLLAIkLn exp1exp (A.6)

csskyLc LLLLAIkLn 2exp1 (A.7)

where kL (kL ≈ 0.95) is the long-wave radiation extinction coefficient, which is similar to

the extinction coefficient for diffuse radiation with low vegetation, i.e., LAI lower than

0.5 [ Campbell and Norman, 1998]. Ω is the vegetation clumping factor proposed by

Kustas and Norman [1999] for sparsely vegetated areas, which can be set to one when

measured LAI implicitly includes the clumping effect (i.e., LAI from the Moderate

Resolution Imaging Spectroradiometer, MODIS) [Anderson et al., 1997; Norman et al.,

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31

1995; Timmermans et al., 2007), and Ls, Lc and Lsky (W m-2

) are the long-wave

emissions from soil, canopy and sky computed by the Stefan-Boltzman equation based

on measured Ts, derived Tc and measured air temperature and vapour pressure

[Brutsaert, 1982]. For further details about Kustas and Norman [1999] partitioning of

Rn used here see Morillas et al.[2013].

<Insert Figure A1>

The linear agreement between daytime estimates of As and Ac from both methods was

high with a determination coefficient (R2) of 0.92 for As and 0.79 for Ac (Fig. A1A and

B). Mean absolute differences between estimates of As and Ac from both methods were

31.74 Wm-2

and 17.97 Wm-2

for As and Ac respectively during the 144 days tested.

Considering these small differences, the higher complexity of K&N method and the

increment of model inputs that this method implies, we decided that using the LB

method for A partitioning between As and Ac at daytime scale was efficient and

consistent.

Appendix B

To determine the optimal number of days, N, to consider in Eq. 6 and Eq. 7 for

estimating fZhang and fdrying a sensitivity analysis was performed using data of Balsa

Blanca field site. We obtained statistics of PML model performance using fZhang and

fdrying estimated using N values from 4 to 25 and also considering the time period

including 4 four days previous and the four days after the current one (signed as 4_4),

the latter an approach more similar to the originally proposed by Zhang et al. [2010].

Page 32

32

<Insert Table B1>

<Insert Figure B1>

The PML model using fZhang presented a better performance using high N values, with

similar results using N from 16 to 25 (Table B1). Using that range of N values, the

lowest values of MAD (0.23-0.25 mm day-1

) and RMSD (0.30-0.34 mm day-1

) (Fig.

B1A) coincided with the better linear agreement showing a R2 range of 0.40-0.42, slope

range of 1.32-1.51 and intercept values from -0.07 to -0.16 (Fig. B1B).

<Insert Table B2>

<Insert Figure B2>

Considering the modeling of the soil drying process included in fdrying, the PML model

performance also obtained better results using high values of N ( Table B2), but the

lowest mean inaccuracies were obtained using N values from 16 to 20 (Fig. B2A) with

MAD ~0.17 mm day-1

and RMSD ~0.21 mm day-1

. Using N from 16 to 20 also the

linear agreement between model outputs and measured E was improved (Fig. B2B) but

the best linear agreement was obtained using N=16 showing R2=0.47 and the best slope

and intercept values (slope=0.97 and intercept=0.02).

Based on these result we decided that N=16 was the more suited value for daily

estimation of fZhang and fdrying for PML model performance included in this paper.

However, it is important to notice that the model accuracy did not showed a strong

variation of model accuracy under the range of N values studied (Table B1 and Table

B2) with a maximum difference on accuracy of ± 0.1mm day-1

depending on N. This

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33

suggests a low sensitivity of the PML model using fZhang and fdrying to the N value and

that alternative N values could be used without a strong effect on model performance.

7. ACKNOWLEDGEMENTS

This research was funded by the Andalusian regional government projects AQUASEM

(P06-RNM-01732), GEOCARBO (P08-RNM-3721), RNM-6685 and GLOCHARID,

including European Union ERDF funds, with support from Spanish Ministry of Science

and Innovation projects CARBORAD (CGL2011-27493) and CARBORED-2

(CGL2010-22193-C04-02). L. Morillas received a PhD grant and funding for a visit to

CSIRO Marine and Atmospheric Research from the Andalusian regional government.

The authors would like to thank Dr. Philippe Choler for his assistance with

programming parameter optimization in R, Dr. Helen Cleugh for her comments and

support during the stay at CSIRO Marine and Atmospheric Research, Peter Briggs for

his help on the edition of this paper and the anonymous reviewers for providing helpful

and constructive suggestions to improve the manuscript.

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9. FIGURE CAPTIONS

Figure 1. Time series of 8-day accumulated precipitation (P) in mm, actual volumetric soil

water content (SWC) in mm3 mm-3 and 8-day averages of LAI (A and B), 8-day averages of

observed E and potential E in mm day-1 (C and D) and 8-day averages of observed E and

estimated E using PML model with fdrying, fSWC and fZhang respectively during the validation

period in Balsa Blanca site (A,C and E) and in Llano de los Juanes site (B,D and F). The

legends in B, D and F apply to A, C and E respectively.

Figure 2. Scatterplots of estimated E using fdrying (A,B), fSWC (C,D) and fZhang (E,F) respectively

versus observed E in mm day-1. Grey dashed line is 1:1 line and the black line is the line of best

fit for the equation provided in the sub-plot by SMA.

Figure 3. Time series of 8-day averages of observed E and estimated E in mm day-1 using fdrying,

fSWC and fZhang respectively using the total optimization period (A), the growing season of the

optimization period (B) or the non-growing season (C) for optimization of parameters gsx and α.

The legends in A also apply to B and C.

Figure A1. Scatterplots of estimated canopy available energy, Ac using Kustas and Norman

[1999] method (K&N) versus the Beer- Lambert Law (BL) (A) and of soil available energy, As

estimated by the same two methods (B). Grey dashed line is 1:1 line and the black line is the

line of best fit for the equation provided in the sub-plot.

Figure B1. Sensitivity of the PML model performance using fZhang to the N value considered for

computing fZhang. N values ranged from 4 to 25 and also considering the time period

including 4 four days previous and the four days after the current one (signed as 4_4).

Effects over RMSD and MAD values (mm day-1) of model performance (A) and over the linear

agreement, represented by slope, intercept and R2, between estimates and EC-derived E values

(B) are shown.

Figure B2. Sensitivity of the PML model performance using fdrying to the N value considered for

computing fdrying. N values ranged from 4 to 25 and also considering the time period

including 4 four days previous and the four days after the current one (signed as 4_4).

Effects over RMSD and MAD values (mm day-1) of model performance (A) and over the linear

agreement, represented by slope, intercept and R2, between estimates and EC-derived E values

(B) are shown.

Page 40

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Est

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(fd

ryin

g)

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Balsa Blanca Llano de los Juanes

R2 = 0.24 y = 0.84x + 0.08

B

R2 = 0.54 y = 1.53x + 0.03

A

R2 = 0.31 y = 0.77x + 0.12

D

R2 = 0.41 y = 1.51x − 0.16

C

R2 = 0.59 y = 0.79x + 0.05

F

R2 = 0.47 y = 0.98x + 0.01

E

Page 42

0

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E (

mm

day

-1)

Optimizing in the growing season

B

0

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mm

day

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Optimizing in the total period

Observed EEstimated E (fdrying)Estimated E (fSWC)Estimated E (fZhang)

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C

Observed E

Estimated E (fdrying) Estimated E (fSWC) Estimated E (fZhang)

Page 43

y = 0.64x + 13.79 R² = 0.79

-50

0

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L (W

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Ac K&N (W m-2)

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(W m

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Page 44

R2

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day

-1

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PML model with fZhang

MAD

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R2slopeinterceptB R2

A

Page 45

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PML model with fdrying

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Page 46

Table 1. Details of field sites used to evaluate the PML model

performance. Quantitative data were derived using data from the entire

study period (Table 2).

Field site: Balsa Blanca Llano de los Juanes

Latitude/Longitude 36º56'21.39"N;

2º02'0122"W

36º55’41.7’’N;

2º45’1.7’’W

Study period October 2006 -

December 2008

April 2005-

December 2007

Elevation (m) 196 1600

Vegetation classification

(IGBP Class) Closed shrubland

Dominant species Stipa tenacissima

Festuca scariosa,

Genista pumila,

Hormatophiylla

spinosa

LAI (MODIS) 0.19-0.67 0.12-0.56

Cover fraction 0.6 0.5

Mean canopy height (m) 0.7 0.5

Mean annual

precipitation (mm) 319 326

Temperature

(˚C)

Min 33 31

Mean 17 13

Max 4 -7

Dryness

Index* 2.8 2.3

Soil depth (m) 0.15-0.25 0.15-1.00

(highly variable)

*Dryness index calculated as the average of the annual dryness index (Eeq/P)

[Budyko, 1974] for the total study period (Table 2).

Page 47

Table 2. Optimization and validation periods used in both field sites. Experimental field site Optimization period Validation period

Balsa Blanca 18 October 2006 18 October 2007

(N=365 days)

19 October 2007 31 December 2008

(N = 440 days)

Llano de los Juanes 27 March 2007

31 December 2007 (N=279 days)

4 April 2005 24 March 2006 (N = 355 days)

Page 48

Table 3. Optimized model parameters and statistic of model performance for the whole validation period (N= 440 days in Balsa Blanca and N = 355 days in Llano de los Juanes). Balsa Blanca fSWC fZhang fdrying gsx 0.0097 0.0067 0.0080 α N/A N/A 0.137 MAD 0.32 0.25 0.17 RMSD 0.41 0.34 0.22 % syst. difference 52 5 18 % unsyst. difference 49 95 82 Eavg* (0.49±0.28) 0.78±0.42 0.58±0.42 0.49±0.27 Llano de los Juanes fSWC fZhang fdrying gsx 0.0076 0.0093 0.0109 α N/A N/A 0.478 MAD 0.25 0.22 0.17 RMSD 0.34 0.31 0.24 % syst. difference 40 45 42 % unsyst. difference 61 56 58 Eavg* (0.56 ± 0.35) 0.55±0.31 0.55±0.30 0.56±0.37 * Eavg mean observed value of daily evapotranspiration (mm day-1) during the validation period in brackets and mean estimated values from each f approach. N/A, not applicable parameter.

Page 49

Table 4. Estimated model parameters by optimizing using the original optimization period, the growing season or the non-growing season a.

Parameter Optimization

period Dates N f estimation method

fSWC fZhang fdrying gsx

Original 27 March 2007 279 0.0076 0.0093 0.0109 α 31 December 2007 N/A N/A 0.478

gsx Growing Season

18 April 2007 109 0.0088 0.0098 0.0105

α 5 August 2007 N/A N/A 0.500 gsx Non-Growing

Season 10 August 2007

134 0.0015 0.0055 0.0099

α 22 December 2007 N/A N/A 0.434 a Abreviations as follows: gsx, maximum conductance of leaves; α, soil drying speed; and N/A, not applicable parameter.

Page 50

Table B1. Statistics of PML model performance with fZhang using different N values. The value of gsx obtained by

optimization in the optimization period (Table 2) is also presented for each N value used for fZhang estimation.

RMSD and MAD values in mm day-1.

PML with fZhang

N 4 6 8 10 12 14 16 18 20 25 4_4

gsx 0.0095 0.0089 0.0085 0.0079 0.0076 0.0076 0.0067 0.0065 0.0061 0.0058 0.0087

R2 0.26 0.30 0.32 0.33 0.34 0.39 0.41 0.42 0.42 0.40 0.19

intercept -0.16 -0.22 -0.24 -0.27 -0.22 -0.18 -0.16 -0.12 -0.10 -0.07 -0.21

slope 1.38 1.58 1.67 1.75 1.66 1.60 1.51 1.44 1.37 1.32 1.58

RMSD 0.34 0.38 0.40 0.41 0.39 0.37 0.34 0.32 0.31 0.30 0.41

MAD 0.26 0.27 0.27 0.27 0.27 0.26 0.25 0.24 0.23 0.23 0.29

*N=4_4 considers the time period including 4 four days previous and the four days after the current one.

Page 51

Table B2. Statistics of PML model performance with fdrying using different N values. The value of gsx and α obtained

by optimization in the optimization period (Table 2) is also presented for each N value used for fdrying estimation.

RMSD and MAD values in mm day-1.

PML with fdrying

N 4 6 8 10 12 14 16 18 20 25 4_4

gsx 0.0100 0.0091 0.0087 0.0082 0.0082 0.0074 0.0080 0.0077 0.0072 0.0059 0.0099

α 0.278 0.259 0.199 0.152 0.142 0.125 0.137 0.105 0.092 0.073 0.247

R2 0.33 0.34 0.36 0.42 0.46 0.48 0.47 0.50 0.51 0.48 0.33

intercept -0.06 -0.08 -0.10 -0.10 -0.05 -0.03 0.02 0.04 0.04 0.02 -0.07

slope 1.23 1.20 1.24 1.27 1.17 1.08 0.97 0.96 0.95 0.94 1.22

RMSD 0.30 0.29 0.29 0.28 0.25 0.23 0.22 0.21 0.21 0.21 0.29

MAD 0.22 0.21 0.21 0.20 0.19 0.18 0.17 0.17 0.16 0.16 0.22

*N=4_4 considers the time period including 4 four days previous and the four days after the current one.