WATER RESOURCES RESEARCH, VOL. 49, 1–15, doi:10.1002/wrcr.20468, 2013
Improving evapotranspiration estimates in Mediterranean drylands:
The role of soil evaporation
Laura Morillas,1 Ray Leuning,2 Luis Villagarcıa,3 Monica Garcıa,4,5 Penelope Serrano-Ortiz,1
and Francisco Domingo1
Received 31 August 2012; revised 6 August 2013; accepted 10 August 2013.
[1] 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
semiarid 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 day1) 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.
Citation: Morillas, L., R. Leuning, L. Villagarcıa, M. Garcıa, P. Serrano-Ortiz, and F. Domingo (2013), Improving evapotranspiration
estimates in Mediterranean drylands: The role of soil evaporation, Water Resour. Res., 49, doi:10.1002/wrcr.20468.
1.
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 E 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 E (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
Introduction
[2] Evapotranspiration (E), is the largest term in the terrestrial water balance after precipitation. Additionally, its
energetic equivalent, the latent heat flux (E), 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
1
Estacion Experimental de Zonas Aridas,
Consejo Superior de Investigaciones Cientıficas (CSIC), Ctra. de Sacramento s/n La Ca~
nada de San
Urbano, Almerıa, Spain.
2
CSIRO Marine and Atmospheric Research, Canberra, ACT, Australia.
3
Departamento de Sistemas Fısicos, Quımicos y Naturales, Universidad
Pablo de Olavide, Sevilla, Spain.
4
Department of Geosciences and Natural Resource Management,
University of Copenhagen, Copenhagen K, Denmark.
5
International Research Institute for Climate and Society, The Earth
Institute, Columbia University, Palisades, New York, USA.
Corresponding author: L. Morillas, Estacion Experimental de Zonas
Aridas,
Consejo Superior de Investigaciones Cientıficas (CSIC), Ctra. de
Sacramento s/n La Ca~nada de San Urbano, Almerıa ES-04120, Spain.
([email protected])
©2013. American Geophysical Union. All Rights Reserved.
0043-1397/13/10.1002/wrcr.20468
1
MORILLAS ET AL.: EVAPOTRANSPIRATION ESTIMATION IN MEDITERRANEAN DRY LANDS
tems as semiarid grasslands and shrublands [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.,
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 types 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
satellite data [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 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; Garcıa 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 (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 parameter in a daily time
basis and consequently proposed an alternative formulation
for f based on Apparent Thermal Inertia using surface
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 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 (Gs), the inverse of the resistance of the soilcanopy 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 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-meansquare error of 0.27 mm day1) 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
day1) 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 [NoyMeir, 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 ecosys2
MORILLAS ET AL.: EVAPOTRANSPIRATION ESTIMATION IN MEDITERRANEAN DRY LANDS
Table 1. Details of Field Sites Used to Evaluate the PML Model Performancea
Field Site
Latitude/Longitude
Study period
Elevation (m)
Vegetation classification (IGBP Class)
Dominant species
LAI (MODIS)
Cover fraction
Mean canopy height (m)
Mean annual precipitation (mm)
Temperature ( C)
Min
Mean
Max
Dryness indexb
Soil depth (m)
Balsa Blanca
0
00
0
Llano de los Juanes
00
36 550 41.700 N; 2 450 1.700 W
Apr 2005 to Dec 2007
1600
36 56 21.39 N; 2 02 0122 W
Oct 2006 to Dec 2008
196
Closed shrubland
Stipa tenacissima
0.19–0.67
0.6
0.7
319
Festuca scariosa, Genista pumila,
Hormatophiylla spinosa
0.12–0.56
0.5
0.5
326
33
17
4
2.8
0.15–0.25
31
13
7
2.3
0.15–1.00 (highly variable)
a
Quantitative data were derived using data from the entire study period (Table 2).
Dryness index calculated as the average of the annual dryness index (Eeq/P) [Budyko, 1974] for the total study period (Table 2).
b
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 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 semiarid 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,
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 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 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.
2.
E ¼ Ec þ Es
ð1Þ
[11] The fluxes of latent heat associated with Ec and Es
were written by Leuning et al. [2008] as
E ¼
"Ac þ cp = Da Ga
"As
þf
" þ 1 þ Ga =Gc
"þ1
ð2Þ
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 m2) are the energy absorbed by the canopy
and soil, respectively. Ga and Gc (m s1) are the aerodynamic and canopy conductances, as defined below. " (kPa
K1) is the slope (s) of the curve relating saturation water
vapor pressure to air temperature divided by the psychrometric constant (), (kg m3) is air density, cp (J kg K1)
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 ¼ esat e).
The factor f in the second term of equation (2) modulates
potential evaporation rate at the soil surface expressed by
the Priestley-Taylor equation, Eeq;s ¼ "As =ð" þ 1Þ, by f ¼ 0
when the soil is dry, to f ¼ 1 when the soil is completely
wet. In spite of the Priestley-Taylor formulation was
designed to estimate potential evaporation in energylimited ecosystems [Priestley and Taylor, 1972], recent
works have demonstrated that accurate estimates of actual
E can be determined in water-limited conditions by
Model Description
2.1. Penman-Monteith-Leuning Model (PML)
Description
[10] 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
3
MORILLAS ET AL.: EVAPOTRANSPIRATION ESTIMATION IN MEDITERRANEAN DRY LANDS
Figure 1. Time series of (a and b) 8-day accumulated precipitation (P) in mm, actual volumetric soil water
content (SWC) in mm3 mm3 and 8-day averages of LAI, (c and d) 8-day averages of observed E and potential E in mm day1, (e and f) 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 Figures 1b, 1d, and 1f apply to Figures 1a, 1c, and 1e, respectively.
2011 when infrared sensors were available to measure surface temperature and shortwave incoming radiation.
Because of these reduced differences (Figure A1) at daytime scale, the Beer-Lambert method was used to maintain
the reduced number of PML model inputs. Of far greater
importance is correctly estimating f, as discussed below.
[13] Aerodynamic conductance Ga is estimated using
[Monteith and Unsworth, 1990]
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.
[12] 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 ¼ A and canopy available energy is
Ac ¼ A(1 ), where ¼ exp(-kALAI) and kA is the extinction coefficient for total available energy A. When eddy covariance data are used for validation, A ¼ H þE 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 the Beer-Lambert 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 m2 for Ac and As, respectively) over 144 days in
Ga ¼
k2u
ln½ðzr d Þ=zom ln½ðzr d Þ=zov ð3Þ
where k is Von Karman’s constant (0.40), u (m s1) 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 equation (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 semiarid 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
4
MORILLAS ET AL.: EVAPOTRANSPIRATION ESTIMATION IN MEDITERRANEAN DRY LANDS
general relations given by Allen [1986]: d ¼ 0.66 h,
zom ¼ 0.123 h, and zov ¼ 0.1.
[14] Canopy conductance was estimated using Leuning et al.
[1995] formulation, based on Kelliher et al. [1995], as follows,
"
#
gsx
Qh þ Q50
1
Gc ¼
ln
kQ
Qh exp kQ LAI þ Q50 1 þ Da =D50
over successive 8 day intervals using accumulated values
of P and Eeq,s in N ¼ 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 ¼ 16, between day i and 15 preceding days (i 15), to estimate daily f using measured values of P and Eeq,s and it is expressed as,
ð4Þ
0
where kQ, is the extinction coefficient of visible radiation,
gsx (m s1) is the maximum conductance of the leaves at
the top of the canopy, Qh (W m2) is the visible radiation
reaching the canopy surface that can be approximated as
Qh ¼ 0.8A [Leuning et al., 2008] and Q50 (W m2) 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 ¼ 30 Wm2, D50 ¼ 0.7 kPa,
and kQ ¼ kA ¼ 0.6 following the sensitivity analysis presented in Leuning et al. [2008].
[15] The PML model (equations (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 section 2.2 were evaluated for improving
PML performance in drylands.
fZhang
fSWC
1
Pi
B
C
B i15
C
B
¼ minB i
; 1C
C
X
@
A
Eeq;s;i
ð6Þ
i15
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)
[20] 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 use a similar formulation for the soil drying periods during dry days in combination with the fZhang method (equation
(7)) used here to estimate f during the effective precipitation
days (Pi > Pmin ¼ 0.5 mm day1). This is,
2.2. Methods for f Estimation
[16] Evaporation from soil surfaces is mainly controlled by
volumetric soil water content in the top soil layer [Anadranistakis et al., 2000; Farahani and Bausch, 1995] and has been
traditionally described occurring in three stages. An energylimited stage (Stage 1) when enough soil water is available to
satisfy the potential evaporation rate (f ¼ 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 ¼ 0)
[Idso et al., 1974; Ventura et al., 2006]. We tested three different methods to capture this dynamic of f.
2.2.1. f As a Function of Soil Water Content Data
(fSWC)
[17] We used measured values of volumetric soil water
content measured at 4 cm depth (obs) rescaled between a
minimum (min) and a maximum (max) threshold value to
estimate f following the expression,
8
¼ 1 when; obs > max
>
<
¼ 0 when; obs < min
>
: ¼ obs -min when; min obs max
max -min
i
X
0
0
1
i
X
Pi
B
B
C
B
B
C
B ¼ minB i15
C when P i > Pmin
;
1
i
BX
C
fdrying B
B
@
A
B
Eeq;s;i
@
i15
¼ fLP expð-DtÞ
when P i >Pmin
ð7Þ
where fLP is the f value for the last effective precipitation
day, Dt is number of days between this and the current day
i and (day1) is a parameter controlling the rate of soil
drying, higher values reflecting higher soil drying speed.
For simplicity, was considered a constant estimated by
optimization, even though it is known that is related to
air temperature, wind speed, vapor pressure deficit, and soil
hydraulic properties [Ritchie, 1972].
3.
ð5Þ
Material and Methods
3.1. Validation Field Sites and Measurements
[21] 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].
[22] 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,
[18] min was experimentally estimated as the minimum
value of the dry season and max as the value of 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)
[19] 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 day1, over
N days. While the original formulation of Zhang et al.
[2010] was designed to estimate the averaged value of f
5
MORILLAS ET AL.: EVAPOTRANSPIRATION ESTIMATION IN MEDITERRANEAN DRY LANDS
vided 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 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 five and three
observations at Balsa Blanca site and Llano de los Juanes,
respectively) which were replaced by the average of previous and subsequent LAI values.
Table 2. Optimization and Validation Periods Used in Both Field
Sites
Experimental Field Site
Optimization Period
Validation Period
Balsa Blanca
18 Oct 2006
18 Oct 2007
N ¼ 365 days
19 Oct 2007
31 Dec 2008
N ¼ 440 days
Llano de los Juanes
27 Mar 2007
31 Dec 2007
N ¼ 279 days
4 Apr 2005
24 Mar 2006
N ¼ 355 days
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 ¼ 3.5 and zr ¼ 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 postprocessing, as was the conversion to half-hour means following Reynolds’ rules [Moncrieff et al., 1997]. The slope of
the linear regressions between available energy (Rn G)
and the sum of the surface fluxes (H þ E) 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].
[23] Complementary meteorological measurements were
also made at each field site. An NR-Lite radiometer (Kipp
& Zonen, 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, Seattle,Wa, USA) 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 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 62.5%
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 data loggers (Campbell CR1000 and Campbell
CR3000 data loggers, Campbell Scientific Inc., USA) and
daytime (from sunrise to sunset) averages were used for
model running.
3.3. Model Performance Evaluation
[25] 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 data sets were divided into an
optimization period, to estimate locally specific gsx and values using the rgenoud package for the R software environment [Mebane and Sekhon, 2011], 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 that minimized the cost function F for
the total sample number, N, included in the optimization
period (See N values in Tables 2 and 4), that is :
XN
F¼
i¼1
jEest;i Eobs;i j
N
ð8Þ
where Eest,i is estimated E for day i and Eobs,i is observed E
for same day.
[26] 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] is used for quantitative evaluation of PML
model results, while root mean square difference (RMSD)
is 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
[27] The two studied sites are Mediterranean drylands
with clear functional differences (Figures 1a and 1b). 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 was more fluctuating at Balsa Blanca where E
3.2. Remotely Sensed Data
[24] LAI estimates were level 4 Moderate Resolution
Imaging Spectrometers (MODIS) composite products pro6
MORILLAS ET AL.: EVAPOTRANSPIRATION ESTIMATION IN MEDITERRANEAN DRY LANDS
(Figures 1e and 1f). 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 day1 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 section 5.
[31] Estimated values of daily E from the PML model
are compared to observations at both field sites in Figure 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 ¼ 0.47) using fdrying was slightly lower than with fSWC
(R2 ¼ 0.54) at Balsa Blanca. Despite the better correlation
achieved using fSWC, this method tended to overestimate E
values (Figure 2a), a problem not found using fdrying (Figure
2e). The highest correlation at Llano de los Juanes was
again obtained using fdrying (R2 ¼ 0.59), whereas using fSWC
and fZhang produced two clusters of high and low predictions (Figures 2b and 2d) and hence poor coefficients of
determination (R2 ¼ 0.24 and R2 ¼ 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 day1) reduced the linear agreement
resulting in a linear regression slope of 0.79 (Figure 2f).
[32] Additional analyses were performed to determine if
the systematic underestimation of E found at Llano de los
Juanes during the growing season (Figure 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 data set periods
showing a very different vegetation activity at this strongly
seasonal site (the growing and the nongrowing season)
(Figure 1b), parameters optimizations were performed
using specific periods (Table 4).
[33] Our results showed that estimates of model parameters
(gsx and ) 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 nongrowing season using
fSWC and fZhang but strongly increased the underestimates of E
for the growing season (Figure 3c). Thus, improvement of
model performance during the dry and growing season of the
validation period was not found using model parameters
Table 3. Optimized Model Parameters and Statistic of Model Performance for the Whole Validation Period (N ¼ 440 Days in Balsa
Blanca and N ¼ 355 Days in Llano de los Juanes)
fSWC
fZhang
fdrying
Balsa Blanca
gsx
MAD
RMSD
% Syst. difference
% Unsyst. difference
Eavga (0.49 6 0.28)
0.0097
N/A
0.32
0.41
52
49
0.78 6 0.42
0.0067
N/A
0.25
0.34
5
95
0.58 6 0.42
0.0080
0.137
0.17
0.22
18
82
0.49 6 0.27
Llano de los Juanes
gsx
MAD
RMSD
% Syst. difference
% Unsyst. difference
Eavga (0.56 6 0.35)
0.0076
N/A
0.25
0.34
40
61
0.55 6 0.31
0.0093
N/A
0.22
0.31
45
56
0.55 6 0.30
0.0109
0.478
0.17
0.24
42
58
0.56 6 0.37
Eavg mean observed value of daily evapotranspiration (mm day1) during the validation period in brackets and mean estimated values from each
f approach. N/A, not applicable parameter.
a
was more strongly linked to the SWC (Figures 1a and 1c),
than at Llano de los Juanes where phenology was the main
factor controlling E (Figures 1b and 1d).
[28] 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 s1) (Table 3). On the other hand,
¼ 0.137 day1 at Balsa Blanca was considerably lower
than ¼ 0.478 day1 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
max and min for applying fSWC were max ¼ 0.20 m3 m3
and min ¼ 0.05 m3 m3 at Balsa Blanca, and max ¼ 0.35 m3
m3 and min ¼ 0.10 m3 m3 at Llano de los Juanes.
[29] Predictions of E obtained using the PML model
with fdrying were superior to both fSWC and fZhang, yielding
the lowest values of MAD (0.17 mm day1) and RMSD
(0.22–0.24 mm day1) 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%).
[30] Using fSWC the PML model resulted in strong overestimations of E following heavy rainfall at both field sites
Table 4. Estimated Model Parameters by Optimizing Using the Original Optimization Period, the Growing Season or the Nongrowing
Seasona
f Estimation Method
Parameter
gsx
gsx
gsx
Optimization
Period
Original
Growing season
Nongrowing
season
Dates
N
fSWC
fZhang
fdrying
27 Mar 2007
31 Dec 2007
18 Apr 2007
5 Aug 2007
10 Aug 2007
22 Dec 2007
279
0.0076
N/A
0.0088
N/A
0.0015
N/A
0.0093
N/A
0.0098
N/A
0.0055
N/A
0.0109
0.478
0.0105
0.500
0.0099
0.434
109
134
a
Abreviations as follows: gsx, maximum conductance of leaves; , soil drying speed; and N/A, not applicable parameter.
7
MORILLAS ET AL.: EVAPOTRANSPIRATION ESTIMATION IN MEDITERRANEAN DRY LANDS
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 codominated by perennial grasses, Festuca scariosa (Lag.) Hackel (19%), and shrubs, Genista pumila ssp
pumila (11.5%) and Hormatophylla spinosa (L). P. K€upfer
(6.3%) [Serrano-Ortiz et al., 2007, 2009]. At this montane
site, extraction of water by shrubs from deep cracks and fissures in the bedrock has been previously detailed [Canton
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.
optimized specifically for those conditions (Figure 3b). This
test also showed a low sensitivity of the optimization method
to the time period used especially using fdrying (Table 4).
5.
Discussion
[34] 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 in Llano de los Juanes (Figure 1). These results can be
understood considering the vegetation composition and geomorphological characteristics of both field sites.
[35] 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
Figure 2. Scatterplots of estimated E using (a, b) fdrying, (c, d) fSWC, and (e, f) fZhang, respectively, versus observed E in mm day1. Gray dashed line is 1:1 line and the black line is the line of best fit for the
equation provided in the subplot by SMA.
8
MORILLAS ET AL.: EVAPOTRANSPIRATION ESTIMATION IN MEDITERRANEAN DRY LANDS
with measured E at Llano de los Juanes (Figure 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
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 min and max. 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
min and max. 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 ¼ 0.0076 m s1) 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 (Figure 1f). As Figure 3b
shows, a higher gsx value (gsx ¼ 0.0088 m s1) derived
from optimization in the growing season (Table 3) reduced
the aforementioned underestimates during that period using
fSWC (Figure 3b). In contrast, during the wet season (November to March 2006) using fSWC led to overestimates of
E (Figure 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.
5.2. Using Precipitation and Equilibrium Evaporation
to Estimate Soil Evaporation (fZhang)
[37] Use of fZhang in the PML model resulted in a strong
overestimation of E during periods following heavy or
intermittent rain events (Figures 1e and 1f). Thus, we found
generally low correlations with observations at both field
sites (Figures 2c and 2d). This occurred because fZhang
(equation (6)) assumes that the effect of rain over the soil
water availability is limited to a time period of N days
(N ¼ 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 ¼ 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
day1 for a sparsely vegetated savanna site in Australia
(Virginia Park) where the mean annual E (1.20 mm day1)
Figure 3. Time series of 8 day averages of observed E
and estimated E in mm day1 using fdrying, fSWC, and fZhang,
respectively, using (a) the total optimization period, (b) the
growing season of the optimization period, (c) or the nongrowing season for optimization of parameters gsx and .
The legends in Figure 3a also apply to Figures 3b and 3c.
5.1. Using Soil Water Content Data to Estimate Soil
Evaporation (fSWC)
[36] 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 (equation (5))
provided unsatisfactory estimates of E (Table 3). This
method tended to systematically overestimate E at Balsa
Blanca (Figure 2a) and presented a poor linear agreement
9
MORILLAS ET AL.: EVAPOTRANSPIRATION ESTIMATION IN MEDITERRANEAN DRY LANDS
mm day1, respectively, the same model reached higher
inaccuracies than ours, with RMSD values of 1.10 mm
day1 (R2 ¼ 0.02) and 0.31 mm day1 (R2 ¼ 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 remotesensing data in drylands where E modeling is still a challenging task [Domingo et al., 2011].
[39] Like fZhang, fdrying shares the advantage of only
requiring widely available precipitation and equilibrium
evaporation data, with the expense of a single additional
parameter . With the use of fdrying, the PML model was
able to capture the varying controls on Es at both field sites
(Figures 1e and 1f). Thus, the optimized value of the parameter, representing the speed at which soil reduces the
capacity to evaporate water, was lower at Balsa Blanca
( ¼ 0.137 day1) than at Llano de los Juanes ( ¼ 0.478
day1). 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 [Canton et al., 2010; Contreras, 2006].
[40] 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 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.
[41] The systematic underestimation of E by the PML
model at the beginning of the dry season observed at Llano
de los Juanes (Figure 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 (Figure 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 ¼ 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.
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 day1. Since the mean annual
was 0.49 mm day1 at Balsa Blanca and 0.56 mm day1 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.
5.3. Modeling the Soil Drying Process to Estimate Soil
Evaporation (fdrying)
[38] Adoption of the fdrying method clearly improved
PML model performance at both sites (Table 3), outperforming the other two approaches (fSWC and fZhang) (Figures
1e and 1f). 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 (equation
(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 day1 and R2 from
0.47 to 0.59 (Figures 2e and 2f). 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 E (R2 0.8) at those two same Australian sites. However, their model overpredicted E during
low E periods [Fisher et al., 2008] similarly to the overestimations that we found at Balsa Blanca site (when E was
lower than 0.2 mm day1) (Figure 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 ¼ 0.32)
when remote sensed surface temperature and albedo from
SEVIRI (Spinning Enhanced Visible and Infared Imager)
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
day1 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 day1 [Mu et al., 2011]. Eventhough, in
two shrubland sites, where observed E was 1.04 and 0.19
6.
Conclusion
[42] The capacity of Penman-Monteith-Leuning model
(PML model) to estimate daily evaporation in sparsely
vegetated drylands is demonstrated through the
10
MORILLAS ET AL.: EVAPOTRANSPIRATION ESTIMATION IN MEDITERRANEAN DRY LANDS
development of methods for temporal estimation of the soil
evaporation parameter f. We advanced 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.
[43] 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 in the PML model and the robustness of
optimization period to estimate model parameters.
AsK&N ¼ Rns G
ðA3Þ
AcK&N ¼ Rnc
ðA4Þ
where Rns and Rnc are daytime averaged estimates from
equations (A(5)) and (A(6)) and G is daytime averaged soil
heat flux from measurements (section 3.1).
Rns ¼ Lns þ s ð1 s ÞS
ðA5Þ
Rnc ¼ Lnc þ ð1 s Þð1 c ÞS
ðA6Þ
where S (W m2) is the incoming shortwave radiation,
s is solar transmittance through the canopy, s is soil
albedo, c is the canopy albedo. Estimates of s, s,
and c are computed following the equations (15.4)–
(15.11) in Campbell and Norman [1998] and based on
LAI, the reflectances and trasmittances of soil and a
single leaf, and the proportion of diffuse irradiation,
assuming that the canopy has a spherical leaf angle
distribution.
[47] Lns and Lnc (W m2) are the net soil and canopy
long-wave radiation, respectively, estimated using the following expressions:
Appendix A
[44] 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 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].
[45] To estimate As and Ac using the Beer-Lambert law,
AsBL and AcBL were estimated as follows
AsBL ¼ Aexp ðkA LAI Þ
ðA1Þ
AcBL ¼ A½1 exp ðkA LAI Þ
ðA2Þ
Figure A1. Scatterplots of (a) estimated canopy available
energy, Ac, using Kustas and Norman [1999] method
(K&N) versus the Beer-Lambert Law (BL) and (b) soil
available energy, As, estimated by the same two methods.
Gray dashed line is 1:1 line and the black line is the line of
best fit for the equation provided in the subplot.
where kA ¼ 0.6 and A ¼ H þE using daytime measured
averages of H and E [Leuning et al., 2008].
[46] To estimate As and Ac using the method proposed
Kustas and Norman [1999], AsK&N and AcK&N where estimated following equations (A3) and (A4)
11
MORILLAS ET AL.: EVAPOTRANSPIRATION ESTIMATION IN MEDITERRANEAN DRY LANDS
Lns ¼ expðkL LAI ÞLsky þ ½1 expðkL LAI ÞLc Ls ðA6Þ
Lnc ¼ ½1 expðkL LAI Þ Lsky þ Ls 2Lc
ðA7Þ
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]. 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., 1995;
Timmermans et al., 2007], and Ls, Lc, and Lsky (W m2) 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 vapor
pressure [Brutsaert, 1982]. For further details about Kustas
and Norman [1999] partitioning of Rn used here see Morillas et al. [2013].
[48] 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 (Figures A1a
and A1b). Mean absolute differences between estimates of
As and Ac from both methods were 31.74 and 17.97 Wm2
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.
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 four 4 days previous and the 4 days after
the current one (signed as 4_4). Effects over RMSD and
MAD values (mm day1) of (a) model performance and (b)
over the linear agreement, represented by slope, intercept,
and R2, between estimates and EC-derived E values are
shown.
Appendix B
[49] To determine the optimal number of days, N, to consider in equations (6) and (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
four 4 days previous and the 4 days after the current one
(signed as 4_4), the latter an approach more similar to the
originally proposed by Zhang et al. [2010].
[50] 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 day1) and RMSD
(0.30–0.34 mm day1) (Figure 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 (Figure B1b).
[51] 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 (Figure B2a) with MAD 0.17 mm
Table B1. Statistics of PML Model Performance With fZhang Using Different N Valuesa
PML with fZhang
N
4
6
8
10
12
14
16
18
20
25
4_4b
gsx
R2
Intercept
Slope
RMSD
MAD
0.0095
0.26
0.16
1.38
0.34
0.26
0.0089
0.30
0.22
1.58
0.38
0.27
0.0085
0.32
0.24
1.67
0.40
0.27
0.0079
0.33
0.27
1.75
0.41
0.27
0.0076
0.34
0.22
1.66
0.39
0.27
0.0076
0.39
0.18
1.60
0.37
0.26
0.0067
0.41
0.16
1.51
0.34
0.25
0.0065
0.42
0.12
1.44
0.32
0.24
0.0061
0.42
0.10
1.37
0.31
0.23
0.0058
0.40
0.07
1.32
0.30
0.23
0.0087
0.19
0.21
1.58
0.41
0.29
a
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 day1.
b
N ¼ 4_4 considers the time period including four 4 days previous and the 4 days after the current one.
12
MORILLAS ET AL.: EVAPOTRANSPIRATION ESTIMATION IN MEDITERRANEAN DRY LANDS
Table B2. Statistics of PML Model Performance With fdrying Using Different N Valuesa
PML with fdrying
N
4
6
8
10
12
14
16
18
20
25
4_4b
gsx
R2
Intercept
Slope
RMSD
MAD
0.0100
0.278
0.33
0.06
1.23
0.30
0.22
0.0091
0.259
0.34
0.08
1.20
0.29
0.21
0.0087
0.199
0.36
0.10
1.24
0.29
0.21
0.0082
0.152
0.42
0.10
1.27
0.28
0.20
0.0082
0.142
0.46
0.05
1.17
0.25
0.19
0.0074
0.125
0.48
0.03
1.08
0.23
0.18
0.0080
0.137
0.47
0.02
0.97
0.22
0.17
0.0077
0.105
0.50
0.04
0.96
0.21
0.17
0.0072
0.092
0.51
0.04
0.95
0.21
0.16
0.0059
0.073
0.48
0.02
0.94
0.21
0.16
0.0099
0.247
0.33
0.07
1.22
0.29
0.22
a
The value of gsx and 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 day1.
b
N ¼ 4_4 considers the time period including four 4 days previous and the 4 days after the current one.
day1 and RMSD 0.21 mm day1. Using N from 16 to 20
also the linear agreement between model outputs and measured E was improved (Figure B2b) but the best linear
agreement was obtained using N ¼ 16 showing R2 ¼ 0.47
and the best slope and intercept values (slope ¼ 0.97 and
intercept ¼ 0.02).
[52] Based on these results, we decided that N ¼ 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 (Tables B1 and B2) with a
maximum difference on accuracy of 60.1 mm day1
depending on N. This 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.
[53] Acknowledgments. 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 Philippe Choler
for his assistance with programming parameter optimization in R, 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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