Using precipitation, vertical root distribution, and satellite-retrieved vegetation information to parameterize water stress in a Penman-Monteith approach to evapotranspiration modeling under Mediterranean climate
Abstract
Recent studies have shown that global Penman-Monteith equation based (PM-based) models poorly simulate water stress when estimating evapotranspiration (ET) in areas having a Mediterranean climate (AMC). In this study, we propose a novel approach using precipitation, vertical root distribution (VRD), and satellite-retrieved vegetation information to simulate water stress in a PM-based model (RS-WBPM) to address this issue. A multilayer water balance module is employed to simulate the soil water stress factor (SWSF) of multiple soil layers at different depths. The water stress factor (WSF) for surface evapotranspiration is determined by VRD information and SWSF in each layer. Additionally, four older PM-based models (PMOV) are evaluated at 27 flux sites in AMC. Results show that PMOV fails to estimate the magnitude or capture the variation of ET in summer at most sites, whereas RS-WBPM is successful. The daily ET resulting from RS-WBPM incorporating recommended VI (NDVI for shrub and EVI for other biomes) agrees well with observations, with
(
18.72
) for all 27 sites and
(
18.21
) for 25 nonagricultural sites. However, combined results from the optimum older PM-based models at specific sites show
(
20.74
) for all 27 sites. RS-WBPM is also found to outperform other ET models that also incorporate a soil water balance module. As all inputs of RS-WBPM are globally available, the results from RS-WBPM are encouraging and imply the potential of its implementation on a regional and global scale.
Key Points
- Soil water content (SWC) and vertical root distribution (VRD) mutually affect evapotranspiration (ET)
- Simulated SWC by RS-WBPM more reliably reflects water stress than VPD
- The developed RS-WBPM well simulates
in areas having a Mediterranean climate
1 Introduction
Land evapotranspiration (ET) is an important biophysical process and a critical component of the land-atmosphere hydrological cycle, which has a large impact on global climate and meteorology. ET returns approximately 60% of all land precipitation to the atmosphere and consumes approximately half of the solar energy absorbed by the land surface [Jung et al., 2010]. Although on a large scale the proportion of transpiration to evapotranspiration varies within a wide range [Kool et al., 2014; Schlesinger and Jasechko, 2014], global land ET is dominated by transpiration [Jasechko et al., 2013] with approximately
of land ET accounted for transpiration [Schlesinger and Jasechko, 2014] on a global scale. Understanding the distribution of
at spatial scales, from fields to the globe as well as temporal scales from days to years, is essential for bio-geophysical research and natural disaster monitoring [Wang et al., 2006; Tang et al., 2010; Yao et al., 2011]. Multiple methods of ET estimation have been proposed based on field observation and remote sensing (RS) data. However, accurate estimation of
remains a significant challenge [Chen et al., 2014].
A series of global ET models have been proposed in recent years [Wang et al., 2006; Cleugh et al., 2007; Mu et al., 2007; Wang et al., 2007; Fisher et al., 2008; Jung et al., 2009; Wang et al., 2010; Komatsu et al., 2012; Yan et al., 2012; Yao et al., 2015] and all the models have succeeded within different limitations. Based on different physical mechanisms, these models can be classified into four general types: Energy Balance models (EB), Penman-Monteith equation based models (PM-based), Priestley-Taylor equation based (PT-based), and empirical models. EB models, e.g., SEBS [Su, 2002], SEBAL [Bastiaanssen et al., 1998a. 1998b], and TSEB [Norman et al., 1995], are capable of exploiting the high spatial resolution of thermal infrared observations but are vulnerable to uncertainties in the input surface temperature [Cleugh et al., 2007; Timmermans et al., 2007; Anderson et al., 2012; Wang and Dickinson, 2012]. The empirical model is a statistical model that depends on the size of the sample data and has no clear physical mechanisms. Wang et al. [2007] used the vegetation index, temperature, and radiation data to model ET in the Great Plains of America, and the model was improved by including diurnal temperature range to indicate the water stress [Wang and Liang, 2008]. Empirical models are simplified and easy to use, but their performances depend on the representativeness of the samples [Chen et al., 2014]. The PT equation [Priestley and Taylor, 1972], simplified from the PM equation, was also applied to model ET [Wang et al., 2006; Fisher et al., 2008; Miralles et al., 2011; Yao et al., 2013, 2015]. PT-based models use environmental constraint factors, estimated using empirical formulas, to scale an equilibrium ET to the actual ET. Both PT-based and empirical models are easy to use, but neither of them explicitly involves surface conductance factors. Such a simplification may lead to a significant bias, if there is a relatively high decoupling factor (
). This factor explains the degree of coupling between vegetation and atmosphere and varies from 0 to 1 [Ryu et al., 2008], which implies a shift in the controlling factors of evapotranspiration from available energy to atmospheric conditions [Jarvis and McNaughton, 1986; Ma et al., 2015]. PT-based models are based on the assumption that
is nearly 0. However, studies have shown significant seasonal variations in
[Ma et al., 2015; Zhang et al., 2016]; for example, an approximate value of
= 0.5 was observed during the rainy season for the highest alpine steppe [Ma et al., 2015], and an annual value of
= nearly 0.27 was observed at a grass flux site under a Mediterranean climate [Ryu et al., 2008]. Furthermore, with the lack of aerodynamic conductance, PT-based model and empirical models do not well explain the phenomenon that the transpiration rate of plants can increase with an increase in the vapor pressure deficit (VPD) under controlled experimental conditions [Schulze and Küppers, 1979; Forseth and Ehleringer, 1983].





















The water stress factor (WSF) plays an important role in regulating surface conductance [Jarvis, 1976] and parameterizations of water stress for dry climates are important but difficult [Michel et al., 2016]. Water stress is not always estimated well as reliable temporal-continuous soil water content (SWC) observations at a global scale are not available [Vinukollu et al., 2011; Yan et al., 2012]. Different versions of PM-based models return different estimates for the surface conductance and canopy conductance [Cleugh et al., 2007; Mu et al., 2007; Leuning et al., 2008; Zhang et al., 2010; Mu et al., 2011; Yan et al., 2012]. The improved RS-PM model by Mu et al. [2007, 2011] used VPD to indicate soil water stress for the canopy conductance. However, it is questionable that whether the soil moisture controls the air moisture near the surface [Vinukollu et al., 2011; Yan et al., 2012], because air moisture may fail to properly indicate the soil moisture in regions where advection occurs frequently. Other versions of PM-based models, such as those of Leuning et al. [2008] and Zhang et al. [2010], also used VPD to reflect water stress. Vinukollu et al. [2011] demonstrated that the models of Mu et al. [2011] yielded poor performances at the US-Ton and US-Blo flux sites, which are located in the areas having a Mediterranean climate (AMC). Similar results have been reported at the same sites by Mu et al. [2007]. Mu et al. [2011] reported a low correlation coefficient (approximately 0.3) resulting from MOD16 algorithm at three flux sites, US-Me5, US-Me2, and US-SO2, in the AMC, and Michel et al. [2016] reported
values of 0.01 and 0.43 resulting from the same algorithm simulating daily ET at IT-Noe and PT-Mi1 sites, respectively.
Jin et al. [2011] and Yan et al. [2012] used soil moisture information simulated by a water balance module to calculate the water stress when estimating ET. Their models yielded good performances at sites (e.g., US-Ton and US-Blo) located in the AMC. However, their studies did not address the issue that plant transpiration rate is mutually effected by the vertical root distribution (VRD) of plants and soil moisture [Yu et al., 2006]. The soil moisture simulated using their model reflects the overall water condition of a specified top soil layer. However, soil water in depth can contribute considerable amounts of available water to vegetation in water-stressed ground surfaces [Wang et al., 2013; Raab et al., 2015], if there is ample inflow water in the wet season. This indicates a vertical variation in water content along the vertical soil profile. Therefore, biomes with different vertical root distributions may be stressed to different degrees when the entire soil profiles are stressed to the same degree [Shi et al., 2015; Zhang et al., 2015]. However, few recent studies modeling ET have addressed the issue on a large spatial scale. It is of note, however, that the GLEAM model reported by Miralles et al. [2011] addressed such concerns by introducing a three-layer running soil water balance module to simulate WSF for bare soil, short vegetation, and tall vegetation, as evapotranspiration in these three areas is assumed to be dominated by soil moisture in the first layer, the first two layers, and all the three layers, respectively. In addition, the WSF for surface evapotranspiration is determined by the wettest soil layer. This strategy is simple and explicit, and good results have been obtained using the GLEAM model [Miralles et al., 2011]. However, the strategy assumes that short and tall vegetation root at two fixed depths. This assumption may be inappropriate on a global scale, because the VRD of global vegetation has a wide variation [Jackson et al., 1996, 1997]. In addition, as the evapotranspiration rate of a plant is more strongly affected by the vertical distribution of its roots, rather than the exact rooting depth [Yu et al., 2006], it would make better sense to include VRD information along the soil profile when estimating the water stress condition of the plant.
The main objective of this study is, therefore, to propose a novel approach for estimating the water stress factor in a PM-based model estimating ET in the AMC. The mutual effect of VRD and SWC on the evapotranspiration process is addressed in this approach. The primary goals of this study are as follows: (1) to evaluate four older PM-based models using observed data from 27 flux sites in AMC; (2) to develop a new PM-based model driven by RS and meteorological data; in the developed model, a multilayer water balance module is employed to simulate SWC information, and the mutual effect of the VRD and SWC information is considered when calculating the WSF for surface evapotranspiration; and (3) to validate the new model using observed latent heat flux data from 27 flux sites.
2 Methodology
2.1 An RS-PM Model Incorporating VRD Information and a Soil Water Balance Module to Estimate Water Stress: RS-WBPM











However, as it is difficult in practice to obtain global temporal-continuous
information, another indicator, SWC, is used instead. Soil water balance models have previously been used to simulate this indicator [Jin et al., 2011; Miralles et al., 2011; Yan et al., 2012] on regional and global scales, and models incorporating SWC have yielded good results at flux sites in arid regions [Jin et al., 2011; Miralles et al., 2011; Yan et al., 2012]. However, the mutual effect of vertical root distribution and soil moisture has not been well considered. In general, plants with different vertical root distributions respond differently to the same bulk soil water deficit condition [Miralles et al., 2011; Shi et al., 2015; Zhang et al., 2015]. To address this issue, the GLEAM (developed by Miralles et al. [2011]) incorporates a three-layer running water balance model to simulate the WSF for bare soil, short vegetation, and tall vegetation, and water stress for surface evapotranspiration is determined by the wettest layer. Root depth information is considered in GLEAM in a simple way, and VRD information is not explicitly involved.
As VRD has a strong effect on the actual water stress condition of the plant [Yu et al., 2006; Zhang et al., 2015], it is considered preferable to include VRD information when estimating the water stress condition of the plant on a global scale. Therefore, we plan to develop a new PM-based model incorporating a novel approach to calculate the WSF, in which the effect of VRD is considered. The new model aims to improve estimation of the water stress condition of the surface, by including the mutual effect of VRD information and SWC on evapotranspiration. A multilayer running water balance module, modified from that of the GLEAM by Miralles et al. [2011], is used to simulate the SWC of multiple soil layers (Figure 1). The WSF for surface evapotranspiration is the weighted sum of the simulated soil water stress factor of each soil layer. The weight of one soil layer is determined by VRD information of itself and the wettest layer. A one-source PM-based model, of which the surface conductance is parameterized using remote sensing vegetation indices, is employed to estimate the maximum and actual evapotranspiration rate. It is of note that water loss by canopy interception is not considered in the developed model. The primary differences between our new model and GLEAM are listed below.

Flow chart of multilayer water balance module, where subscript t denotes index of period, superscript
denotes soil layer index,
and
represent soil water content and soil water content change, respectively,
is the soil water stress factor,
is the water stress factor for surface evapotranspiration,
is the weight of the soil layer,
is the inflow water source, and
is estimated actual evapotranspiration. The symbol without superscript
denotes the status of the entire soil profile.
- WSF estimation. The WSF in GLEAM is determined by the wettest soil layer, while in the new model it is calculated using the VRD and water content information of each soil layer. The strong effect of the wettest soil layer is also considered.
- The water balance strategy. All specified soil layers in the new model are available for all the vegetation types, whereas in GLEAM only the shallowest two soil layers are available for short vegetation, and all three layers are available for tall vegetation. Additionally, in the new model the evapotranspiration source (with the exception of the bare soil) extracts water from all the specified soil layers during one period. The water loss of each layer is determined by the magnitude of the input water source, actual evapotranspiration, and the weight of the soil layer (see section 2.1.3) during the specified period.
2.1.1 The One-Source RS-PM Model







Yebra et al. [2013] suggested assembling multi-VI to calculate the ET for different biomes. In this study, we employed the normalized difference vegetation index (NDVI) and the enhanced vegetation index (EVI) and compared the performances of the two indices. As reported by Yebra et al. [2013], the EVI best explains variation in
for rain-free days (
), and EVI is recommended for evergreen needle leaf forests (ENF). However,
parameterized with NDVI (
) performs best for most biome types. Although the crop coefficient (Kc) [Guerschman et al., 2009] has been recommended for evergreen broad leaf forests (EBF) and deciduous broad leaf forests (DBF), there are no significant differences in
or RMSE between models parameterized with NDVI and Kc. In addition, the model parameterized with EVI yielded higher
than that with NDVI or Kc. For NDVI, the coefficients of equation 3 are specified as
= 0.002
,
= 4.11, and
= 0.4; and for EVI, the coefficients are
= 0.0025
,
= 3.15, and
= 0.1.







![]() |
GRO | EBF | ENF | DBF | GRA | SHR | SAV |
---|---|---|---|---|---|---|---|
![]() |
1.5 | 0.4 | 1 | 0.55 | 1 | 1 | 1 |
![]() |
1.5 | 0.4 | 1 | 0.65 | 1 | 1 | 1 |
- a CRO: crop, DBF: deciduous broad leaf forest, EBF: evergreen broad leaf forest, ENF: evergreen needle leaf forest, GRA: grassland, SHR: open shrub or closed shrub, and SAV: savannah or woody savannah.
- b
denotes
parameterized with EVI and
denotes
parameterized with NDVI.



Here
is the actual water stress factor for a certain region during a specific period and
is the surface conductance scaled by
2.1.2 Incorporating Vertical Root Distribution Information to Calculate Water Stress Factor





-
WSF incorporating VRD information.
Considering the effect of VRD, WSF is calculated using the information from VRD and the water stress factor of soil layers at multiple depths. Rainfall and snowmelt are considered as the incoming water source,
. (the calculation of snowmelt is referred to in the method adopted by Yan et al. [2012].) The method used to calculate WSF is presented as follows:
(7)
(8)
(9)
(10)
where superscript(11)
denotes the soil layer index, subscript
denotes the index of the period,
represents the water stress factor for evapotranspiration, and
represents the soil water stress factor of soil layer
during period
. Furthermore,
and
denote the input water source (mm) and maximum evapotranspiration rate (mm) during period
is estimated using equations 1 and 4;
,
,
, and
are precipitation (mm), rainfall (mm), snowmelt (mm), and snow depth (water equivalent: mm) during period
;
is the air temperature near the surface (
);
is the water content of soil layer
during period
and is the result of the soil water balance of soil layer
during the last period;
is the wilting point (mm) of soil layer
.
is the critical value of the soil water content when stomatal conductance is at its maximum [Raab et al., 2015] and is set as
in this study, where
is the field capacity of soil layer
,
is the weight of soil layer
during period
, and
, where
is the total number of soil layers.
is determined by the root biomass proportion in the current layer as well as in the wettest layer.
The
for the wettest soil layer is calculated as
where superscript(12)
denotes the index of the wettest layer;
is the proportion of root biomass (
) in the wettest soil layer during period
;
is a factor to enlarge the weight of wettest soil layer (
), where
= 0 indicates that the wettest soil layer is equally weighted with the other layers, and
= 1 indicates that the WSF is totally determined by the wettest soil layer.
is fixed to 0.5 in this study. The
of the remaining layers is calculated as
where(13)
is the proportion of root biomass (
) in soil layer
during period
, and
.
-
Proportion of root biomass,
, in soil layer.
We assume that the pixel of remote sensing images consists of
different components and that
includes VRD information of all these components. Therefore, at a pixel scale, we propose that
is calculated as
where the subscript(14)
denotes the index of the surface component;
represents the proportion of root biomass of surface components
within soil layer
during period
, and
is the fractional cover of surface components
during period
.
To describe the vertical distribution of root biomass of each surface component, the widely used asymptotic equation proposed by Gale and Grigal [1987] is adopted and presented as follows:
where(15)
is the cumulative root biomass proportion (0–1) of the plant below soil depth
(cm) and
is the extinction coefficient (
), which varies among different biome types. High values of
correspond to a greater proportion of root biomass at depth [Jackson et al., 1996, 1997]. Therefore, the root biomass proportion within soil layer
of surface component
,
, is calculated as
where(16)
and
are the depths of the top boundary and bottom boundary of soil layer
, respectively, and
is the root extinction coefficient of surface component
. Specially, for the shallowest layer (
= 1),
= 0, and for the deepest layer, we set
= 0.
In this study, a single pixel is assumed to consist of three components, overstory canopy, understory canopy, and soil surface. The fractional cover of the overstory canopy of woody lands (forest and shrub) during period
,
, is interpreted from high-resolution images of Google earth, and this value is invariant at a specific site in this study. The fractional cover of the understory canopy,
, is calculated as
where(17)
is the total fractional cover of vegetation during period
, which is estimated using the NDVI value retrieved from the MODIS product (see section 2.3.3). We adopt the method proposed by Carlson and Ripley [1997] to estimate
as
where(18)
and
are the
values of bare and full vegetation covered surfaces, respectively, and these two values are specified in Carlson and Ripley [1997] as 0.15 and 0.72. The fractional cover of bare soil during period
,
, is
(19)
The vertical distribution information of fine roots is used in this study. The formation of fine roots is used, rather that of the total root biomass, because the fine root is the primary pathway for water uptake [Jackson et al., 1997].
values for the fine root biomass of temperate biomes calibrated globally by Jackson et al. [1997] is used to calculate VRD information for biomes in areas with a Mediterranean climate. The
value for the fine root biomass of crops is not available [Jackson et al., 1997] and therefore the value for total root biomass calibrated by Jackson et al. [1996] is used.
values for overstory species, understory species, and bare soil of each biome type are specified in Table 2. We assume that all the understory species of woody land is grass and that there is no overstory canopy for grass land and crops. The
value for bare soil is 0; this value indicates that bare soil merely uptakes water from the shallowest soil layer.

Biomes in This Study | Surface Components | Beta | Temperate Biomes |
---|---|---|---|
EBF | Overstory canopy | 0.95 | Sclerophyllous trees |
Understory canopy | 0.943 | Temperate grassland | |
Bare soil | 0 | ||
DBF | Overstory canopy | 0.967 | Temperate deciduous forest |
Understory canopy | 0.943 | Temperate grassland | |
Bare soil | 0 | ||
ENF | Overstory canopy | 0.98 | Temperate coniferous forest |
Understory canopy | 0.943 | Temperate grassland | |
Bare soil | 0 | ||
SHR | Overstory canopy | 0.95 | Sclerophyllous shrubs |
Understory canopy | 0.943 | Temperate grassland | |
Bare soil | 0 | ||
GRA | Overstory canopy | 0 | Temperate grassland |
Understory canopy | 0.943 | Temperate grassland | |
Bare soil | 0 | ||
SAV | Overstory canopy | 0.95 | Sclerophyllous trees |
Understory canopy | 0.943 | Temperate grassland | |
Bare soil | 0 | ||
CRO | Overstory canopy | 0 | |
Understory canopy | 0.961 | Crops | |
Bare soil | 0 |
2.1.3 Multilayer Soil Water Balance Module


- for
10 cm: 0–D;
- for 10 cm
100 cm: 0–10 cm and 10 cm–D;
- for
> 100 cm: 0–10 cm, 10–100 cm, and 100–
.







-
For
, the change in soil water of layer
,
, depends on
and the total loss of water from the entire soil profile, such that
where(21)
is the soil water content (mm) of layer
in the next period.
-
For
,
is calculated as follows:
(22)
where(23)
represents the water infiltrated from layer
to
; and water from layer
to layer
,
, is the residual of
after filling soil layer
(see equation 23). Specially, for the first layer:
=
.
2.1.4 Implementing the Model



- Let
, and use this initial value to simulate time series
values.
- Calculate the 16 day
of each soil layer in each year: the sequence number of 16 day periods in each year is defined as
, where
is the Julian day.
- Interannually average 16 day
with the corresponding sequence number (the first 16 day period is excluded).
- The
value of the first day is assumed to be the interannually averaged
of the corresponding 16 day period.
The DoY of the first day at all the flux sites in this study is 1, and the first interannually averaged 16 day,
, is used at every site. For sites with data covering only 1 year, the last 16 day
of this year is used as
.
2.2 The Older PM-Based Models
Penman [1948] developed the Penman equation. Monteith [1965] improved this equation by introducing surface constraint factors, the surface conductance and resistance to it. The modified equation (PM equation) could be used for vegetated land surfaces. Surface conductance in PM equation is the controlling factor in regulating plant transpiration. Further studies to improve the PM-based model have also focused on the conductance factor [Cleugh et al., 2007; Mu et al., 2007; Leuning et al., 2008; Hu et al., 2013; Yebra et al., 2013]. Shuttleworth and Wallace [1985] developed a two-source PM-based model with a series configuration. This model partitions
into soil evaporation and canopy transpiration. More conductance factors were added to the model. The simulation accuracy for ET has been significantly improved by parameterizing the canopy conductance with the Gross Primary Productivity (GPP) [Hu et al., 2013]. Unfortunately, the coefficients to be determined in this model are only available for individual sites. The PM equation successfully works on well-watered surfaces and has been adopted by the Food and Agriculture Organization of the United Nations (FAO) to calculate the crop reference ET [Allen et al., 1998]. Cleugh et al. [2007] proposed the RS-PM model for regional application. The surface conductance was parameterized with the MODIS LAI product in this model. The RS-PM model was further developed using a parallel two-source configuration by parameterizing the canopy conductance using different strategies [Mu et al., 2007; Leuning et al., 2008; Mu et al., 2011; Yan et al., 2012]. Four older PM-based model are listed in Table 3. They will be evaluated using the observed data at 19 flux sites located in the AMC.
No. | Name | Model Descriptionsa | References |
---|---|---|---|
1 | Mu2011 | MOD16 Algorithm | Mu et al. [2011] |
2 | Ye-VI | See equations 1 and 4 | Cleugh et al. [2007] and Yebra et al. [2013] |
3 | Zh2010 |
![]() |
Leuning et al. [2008] and Zhang et al. [2010] |
4 | Mu2007 |
![]() |
Mu et al. [2007] |
- a
: water stress factor for soil evaporation,
: available energy for canopy transpiration,
: maximum stomatal conductance at the top of the canopy,
: visible radiation at the top of the canopy,
: leaf area index of canopy,
: available energy for soil transpiration,
: relative humidity of air,
: mean stomatal conductance coefficient,
: constraint factor of air temperature to stomatal conductance,
: constraint factor of
to stomatal conductance. For the meaning of other symbols, please see equation 1.



















2.3 Data and Data Processing
2.3.1 Flux Data and Meteorological Data
Daily and half-hourly flux and meteorological data sets of 27 sites located in the AMC (Figure 2) were used to evaluate old version PM-based models and validate the new model. Among these sites, 18 were retrieved from the “FLUXNET LaThuile Dataset 2007” (http://www.fluxdata.org), and the other 9 were from “FLUXNET2015 Dataset” (http://www.fluxdata.org) (Table 4). Half-hourly observations were used to produce daytime and nighttime meteorological data to drive the Mu2011 model. The 27 sites covered the primary biome types in the AMC, of which 6 sites were located in areas with a Mediterranean climate in California (USA) and 21 sites were located in the Mediterranean Sea Basin. These two regions covered most AMC areas on earth. The eddy covariance method (EC) was used for flux observations at all sites. The flux data set provided energy flux (i.e., the latent heat flux (
), sensible heat flux (
), and net radiation (
)) and meteorological variables (e.g., air temperature, relative humidity, saturated vapor pressure deficit, and precipitation).

Distribution of the 27 eddy covariance flux towers used in this study.
Site Name | Site Code | Biome | Lat | Lon | HC (m) | Pa (mm) | Years | References |
---|---|---|---|---|---|---|---|---|
Sites of FLUXNET LaThuile Dataset 2007 | ||||||||
El Saler-Sueca | ES-ES2 | CRO | 39.28 | −0.32 | 1.0b | 525 | 2004–2006 | Carvalhais et al. [2010] |
BorgoCioffi | IT-BCi | CRO | 40.52 | 14.96 | 1.0b | 1336 | 2005–2006 | Moors et al. [2010] |
Collelongo | IT-Col | DBF | 41.85 | 13.59 | 13 | 738 | 2000–2002 | Granier et al. [2000] |
Roccarespampani1 | IT-Ro1 | DBF | 42.41 | 11.93 | 15 | 784 | 2000–2006 | Rey et al. [2002] |
Roccarespampani2 | IT-Ro2 | DBF | 42.39 | 11.92 | 15 | 859 | 2004––2006 | Tedeschi et al. [2006] |
Puechabon | FR-Pue | EBF | 43.74 | 3.6 | 6 | 927 | 2000–2006 | Misson et al. [2011] |
Castelporziano | IT-Cpz | EBF | 41.71 | 12.38 | 12.5 | 795 | 2000–2006 | Tirone et al. [2003] |
Lecceto | IT-Lec | EBF | 43.3 | 11.27 | 8.6 | 242 | 2005–2006 | Stoy et al. [2013] |
Espirra | PT-Esp | EBF | 38.64 | −8.6 | 20 | 658 | 2002–2006 | Granier et al. [2007] |
Mitra(Evora) | PT-Mi1 | EBF | 38.54 | −8 | 7.3 | 478 | 2003, 2005 | Pereira et al. [2007] |
El Saler | ES-ES1 | ENF | 39.35 | −0.32 | 7.28c | 558 | 2000–2006 | Reichstein et al. [2005] |
San Rossore | IT-SRo | ENF | 43.73 | 10.28 | 16 | 562 | 2000–2006 | Granier et al. [2007] |
Blodgett Forest | US-Blo | ENF | 38.9 | −120.63 | 4.7 | 1243 | 2000–2006 | Misson et al. [2007] |
Metolius-old pine | US-Me4 | ENF | 44.5 | −121.62 | 20 | 663 | 2000 | Law et al. [2001] |
Mitra IV Tojal | PT-Mi2 | GRA | 38.48 | −8.02 | 0.25 | 509 | 2005–2006 | Pereira et al. [2007] |
Vaira Ranch-Ione | US-Var | GRA | 38.41 | −120.95 | 0.55 | 563 | 2001–2006 | Ryu et al. [2008] |
Las Majadas del Tietar | ES-LMa | SAV | 39.94 | −5.77 | 8 | 689 | 2004–2006 | Casals et al. [2009] |
Tonzi Ranch | US-Ton | SAV | 38.43 | −120.97 | 7.1 | 573 | 2002–2006 | Ma et al. [2007] |
Sites of FLUXNET2015 Dataset | ||||||||
Laguna Seca | ES-LgS | SHR | 37.1 | −2.97 | 0.2 | 516 | 2007–2009 | Reverter et al. [2010] |
Llano de los Juanes | ES-LJu | SHR | 36.93 | −2.75 | 0.5 | 595 | 2004–2013 | Serrano-Ortiz et al. [2007] |
Sardinia/Arca di Noè | IT-Noe | SHR | 40.61 | 8.15 | 1.2 | 572 | 2004–2012 | Carvalhais et al. [2010] |
Castel d'Asso1 | IT-CA1 | DBF | 42.38 | 12.03 | 3.5–5.5 | 716 | 2012–2013 | PIs (Dario Papale and Simone Sabbatini) |
Castel d'Asso3 | IT-CA3 | DBF | 42.38 | 12.02 | 0.05–3.5 | 644 | 2012–2014 | PIs (Dario Papale and Simone Sabbatini) |
Castelporziano2 | IT-Cp2 | EBF | 41.7 | 12.36 | 14 | 821 | 2012–2013 | Savi et al. [2016] |
Metolius-intermediate aged ponderosa pine | US-Me2 | ENF | 44.45 | −121.56 | 3.6 | 488 | 2002–2014 | Irvine et al. [2007] |
Metolius Young Pine Burn | US-Me6 | ENF | 44.32 | −121.61 | 5.2 | 468 | 2010–2012 | Yan and Shugart [2010] |
Castel d'Asso2 | IT-CA2 | GRA | 42.38 | 12.03 | 0.3 | 715 | 2011–2013 | Reverter et al. [2010] |
- a P was averaged from tower-observed annual precipitation data during the study period.
- b Observed canopy height values for two crop sites were not available in this study, and thus fixed value 1 m was used.
- c
HC value(s) retrieved from global forest canopy height product data set developed by Simard et al. [2011], and corrected using a linear relationship (
, where
and
are observed HC values and modeled HC values at flux sites (m), respectively) derived from a linear regression between available observed HC values and those modeled at flux sites. This relationship is available in Simard et al. [2011].
As temporally continuous meteorological data on a daily step was required for RS-WBPM to derive soil water content information, gaps in daily net radiation (
), temperature (
), saturated vapor pressure deficit (
), and precipitation (
) were filled with values retrieved from the ERA-Interim data set (http://apps.ecmwf.int/datasets/). The retrieved ERA-Interim data had a spatial resolution of 0.125 arc degree, which was far larger than the footprint of the eddy covariance tower. Therefore, there might be significant bias between the meteorological data derived from ERA-Interim and that measured at the flux site, and thus each variable from ERA-Interim was corrected by linear regression with available observations at specific sites. The estimated
by all ET models in this study was compared with site observed
, and daily records with no available half-hourly observations were removed.
2.3.2 Soil Hydrological Properties
The field capacity and the wilting point data of each flux site were extracted from the IGBP-DIS data set [Global Soil Data Task Group, 2000; Global Soil Data Task, 2014], which was available on http://www.daac.ornl.gov. The IGBP-DIS data set had a resolution of 0.0625 arc degree. It provided seven data surfaces that were generated by the Soil Data System developed by the Global Soil Data Task Group of IGBP. All measurements in the IGBP-DIS data set were taken at the depth interval of 0–100 cm. The field capacity and the wilting point were directly available in this data set.
In this study, a multilayer soil water balance model was employed and the field capacity and wilting point of the soil layer (with a vertical thickness of
) were retrieved values scaled by
.
2.3.3 Vegetation Parameters From Remote Sensing Data
Leaf area index (LAI) and two vegetation indices, NDVI and EVI, were used to parameterize surface conductance in this study. The three variables for every flux site were retrieved from the MODIS subset data set available on ORNL DAAC (http://daac.ornl.gov) [ORNL DAAC, 2008]. Blocks centered by the flux tower sites with a size of
were used to extract the LAI pixels from the MOD15A2 collection. Their spatial and temporal resolution were 1 km and 8 days, respectively. The LAI value of the central pixel of the subset block was used as the LAI value of the flux site. LAI values with low confidence were replaced with values obtained by interpolating between the closest reliable values in time, according to the method adopted by Zhao et al. [2005]. The subset block with the same spatial extent at the specific flux site was also used to extract NDVI and EVI. The values of the two VIs for ES-LgS, IT-CA1, IT-CA3, IT-Cp2, and US-Me6 sites were retrieved from the MOD13Q1 (250 m, 16 days) alone, and that for the remaining sites were extracted from both of MOD13Q1 (250 m, 16 days) and MYD13Q1 (250 m, 16 days) collections. There were
pixels in a single NDVI or EVI subset and among them, the pixel where the site located was used. Both of EVI and NDVI were also processed in the same way as that applied to the LAI subset, before they were used.
3 Results
3.1 Performance of Older PM-Based Models in the AMC
Older PM-based models (Table 3) are evaluated against the daily
observed at 27 flux sites located in the AMC. Figure 4 shows the results simulated using the four old version PM-based models (PMOV). Two results are available for the Ye-VI model: results of Ye-VI with
parameterized with EVI (Ye-EVI) and NDVI (Ye-NDVI), respectively. When estimating the VI-based
, equation 4 is incorporated in both Ye-EVI and Ye-NDVI. Figure 3 shows temporal variations of
estimated by the PMOV and that observed at the flux site. It can be concluded from Figure 4 that no single model gives the best performance for all sites or biomes. Among the PMOVs, Ye-EVI gave the optimum performance for CRO (
=
,
=
,
and
denote averaged
and RMSE of all the crop sites, which is the same for other biomes), Ye-NDVI for DBF (
=
,
=
), Zh2010 for EBF (
=
,
=
), and ENF (
=
,
=
), Mu2011 for GRA (
=
,
=
) and Mu2007 for SHR (
=
,
=
) and SAV (
=
,
=
).

Temporal variation in daily
estimated by four PM-based models, and observed flux at 27 flux sites.

Coefficient of determination (
), root mean standard error (RMSE), and bias (Bias) of observed daily
versus estimated
for four older PM-based models on a daily temporal scale at 27 flux sites. Please refer to Table 4 for the data period at each site.
PMOVs reasonably capture the temporal variation of the
at few sites (Figure 3). For most sites, PMOVs tend to yield unreliable estimation for
in summer, especially for sites of SHR, GRA, and SAV (e.g., IT-Noe, ES-LJu, FR-Pue, US-Ton, and US-Var). This may result from unreliable estimation for the water stress. Water supply, primarily from precipitation for naturally grown biomes, is a limiting factor when estimating the actual λE in water-stressed seasons and regions [Hao et al., 2013]. Ryu et al. [2008] reported that the actual λE was constrained by precipitation at the GRA site, US-Var, in the dry season. In the AMC, there is little precipitation but ample solar radiation in summer. This leads to severe water stress for most biomes in the season when vegetation indices reach their peak values of the year. Maselli et al. [2014a, 2014b] demonstrated a similar phenomenon in northern and central Italy. Maselli [2004] found a significant positive correlation between interannual variations in NDVI and precipitation in August and September for pine and oak forests in the Natural Park of Maremma in northwest Italy. The Ye-VI model incorporates NDVI or EVI to reflect the variation of surface conductance while computing
. However, the cross validation or calibration of PM-based models included only a small proportion of the in situ data in the AMC; thus, the calibrated models may not well estimate the water stress under the Mediterranean climate pattern. Of the other three models, Zh2010 underestimated
at most forest sites (e.g., US-Me2, US-Blo, IT-Ro2, and IT-CA3) in summer; Mu2007 and Mu2011 overestimated
at some forest sites (e.g., FR-Pue, IT-Cpz, IT-Ro1, IT-SRo, and US-Me6) whereas underestimated it at other sites (e.g., IT-CA3 and US-Blo). All three models incorporated VPD to reflect water stress on surface conductance, which may introduce uncertainties in simulating water stress.
The ET of CRO was not well estimated by any of the models (Figure 4), as it is not easy to estimate because of areas under irrigation. Velpuri et al. [2013] reported that the MOD16 product underestimated the ET rate of seven CRO flux sites in North America by 10 mm/month. These underestimations may result from a lack of information concerning irrigation. This result is inconsistent with that of Hwang and Choi [2013], who reported that Mu2007 overestimated ET at the HFK flux site with a CRO ecosystem in South Korea. The HFK site is located near the Pacific Ocean, where advection occurs frequently in summer, and it has a temperate climate affected by the wet monsoon. As relative humidity was incorporated to indicate the water stress in Mu2007, the advection of wet air from the ocean could have led to an overestimation of ET.
There are large uncertainties when simulating
of biomes in the AMC using older PM-based models. These uncertainties do not depend just on the biome types, as the performance of the models can vary significantly among sites of a certain biome type (Figure 4). Rather, the uncertainties are likely to be induced by the poor estimations of water stress in the dry season.
3.2 Validation of RS-WBPM at 27 Flux Sites
The RS-WBPM model was then implemented at 27 flux sites located in the AMC (see Table 4), and two model scenarios, RS-WBPM parameterized with EVI (RS-WBPM-EVI) and NDVI (RS-WBPM-NDVI), respectively, were applied. The combined results of the optimum older PM-based model (OMOV) at specific sites are compared with the result of the RS-WBPM, and scatterplots of observed daily
versus estimated
by RS-WBPM-EVI, RS-WBPM-NDVI, and OMOV are shown in Figure 5. Figure 6 shows the temporal variation of observed 16 day
and estimated 16 day
by RS-WBPM-EVI, RS-WBPM-NDVI, and OMOV at eight flux sites. Furthermore, Figure 7 shows the performances of RS-WBPM-EVI, RS-WBPM-NDVI, and OMOV at each site.

Scatterplots of observed daily
versus estimated
by (a) RS-WBPM-EVI: RS-WBPM parameterized with EVI, (b) RS-WBPM-NDVI: RS-WBPM parameterized with NDVI, and (c) OMOV: combined results of optimum model of the old version (OMOV) at specific sites.

Temporal variations in observed 16 day
(observed), estimated
by RS-WBPM parameterized with EVI (RS-WBPM-EVI), RS-WBPM parameterized with NDVI(RS-WBPM-NDVI) and optimum model of the old version (OMOV) at eight flux sites.

Coefficient of determination (
), root mean standard error (RMSE), and bias (Bias) of observed daily
versus estimated
by RS-WBPM-EVI: RS-WBPM parameterized with EVI; RS-WBPM-NDVI: RS-WBPM parameterized with NDVI; and OMOV: optimum model of the old version at particular sites: Ye-EVI for ES-ES2, ITCp2 and ES-ES1; Ye-NDVI for IT-CA3, IT-Col and IT-Ro2; Zh2010 for IT-Rol, FR-Pue, IT-Cpz, PT-Esp, PT-Mi1, IT-SRo, US-Blo, US-Me2, US-Me4 and IT-Noe; Mu2007 for IT-CA1, US-Me6, PT-Mi2, ES-Lgs, ES-LJu, ES-LMa and US-Ton; and Mu2011 for IT-Lec, IT-CA2 and US-Var. Please see Table 4 for the data period associated with each site.
Figure 5 here shows that both RS-WBPM-EVI and RS-WBPM-NDVI outperform OMOV. RS-WBPM-EVI and RS-WBPM-NDVI yield
(
) of 0.59
) and 0.55
) for all 27 sites, respectively, while OMOV yields
(
) of 0.50
). This result also demonstrates that RS-WBPM-EVI better estimates daily
than RS-WBPM-NDVI. However, Figure 7 shows some differences. RS-WBPM-NDVI performs better than RS-WBPM-EVI for SHR with
(
) of 0.53 (
), which implies that RS-WBPM could perform better by assembling EVI and NDVI rather than merely incorporating one of them. Based on the results in Figure 7, we recommend the use of EVI for CRO, DBF, EBF, ENF, GRA, and SAV, and NDVI for SHR.
Figure 7 also shows that RS-WBPM outperforms OMOV for all biomes except for CRO and that the advances of RS-WBPM are more apparent at sites of GRA, SHR, and SAV. Parameterized with the recommended VI, RS-WBPM yields
(
) of 0.64 (15.15
), 0.53 (13.54
), and 0.79 (13.39
) on a daily scale for GRA, SHR, and SAV, respectively, which is 0.20 (1.96
), 0.19 (1.57
), and 0.19 (5.75
) higher (lower) than that of OMOV. With the recommended VI, RS-WBPM yields
(
) of 0.44 (34.94
), 0.78 (21.97
), 0.57 (16.65
), and 0.60 (18.54
) for daily
of CRO, DBF, EBF, and ENF, respectively. In addition, at all 27 sites, it yields
(
) of 0.60
) for daily
(Figure 8a).

Scatterplots of observed daily
versus estimated
by RS-WBPM with suggested VI at (a) all 27 flux sites, and (b) all sites except crop sites. NDVI is used for DBF and SHR; and EVI for CRO, EBF, ENF, GRA, and SAV.
However, we noted that the performance of RS-WBPM is no better than that of OMOV at the two CRO sites, ES-ES2 and IT-BCi, with a relatively large bias. The OMOVs for two crop sites, IT-Bci and ES-ES2, are Ye-EVI and Ye-NDVI, respectively. This demonstrates that the soil WSF simulated by RS-WBPM introduces more uncertainties to CRO. This may be associated with a lack of irrigation information at the two sites in this study. RS-WBPM with recommended VI yields
(
) of 0.62
) for 25 nonagricultural sites (Figure 8b). Results show that Ye-EVI is recommended for calculating evapotranspiration for crop land, because it performs better than the other PMOVs. These results are consistent with those of Jin et al. [2011], whose model yielded better performances for crops when excluding soil water stress information derived from precipitation and a soil water balance model.
Temporal variations of
are better captured by RS-WBPM than OMOV at nonagricultural sites. OMOV significantly overestimates
at ES-ES1, FR-Pue, IT-Noe, US-Ton, and US-Var in the dry season, but underestimates
at US-Blo. Model Zh2010, which incorporates VPD to reflect water stress, is the OMOV for FR-Pue, IT-Noe, and US-Blo. This implies that simulated soil water information by RS-WBPM is more reliable than VPD in reflecting the water stress condition for surface evapotranspiration.
4 Discussion
4.1 A Comparison of RS-WBPM With Models That Incorporate Water Balance Modules and Other Models Using VPD to Reflect Water Stress
Table 5 shows the
of RS-WBPM with recommended VI, PT-JPL, and other models incorporating soil water balance modules at seven flux sites on daily and monthly scales [Fisher et al., 2008; Jin et al., 2011; Miralles et al., 2011; Yan et al., 2012; Michel et al., 2016]. The simulation implemented by Michel et al. [2016] was driven by satellite-retrieved meteorological data which included surface radiation. Satellite-retrieved meteorological data were also used in the simulation by Miralles et al. [2011], but in situ surface radiation was used instead of satellite-retrieved data (Table 5). To avoid overestimating the performance of the RS-WBPM, we reran RS-WBPM using the same radiation inputs as Michel et al. [2016] and Miralles et al. [2011], respectively, and retrieved additional meteorological data from the ERA-Interim data set.
Site | Model |
![]() |
Year | Radiation Data | Meteorological Data | Temporal Scale | References |
---|---|---|---|---|---|---|---|
US-Ton | RS-WBPM-EVI | 0.78 | 2002–2005 | In situ | In situ | Day | This study |
ARTS E | 0.77 | 2002–2005 | In situ | In situ | Day | Yan et al. [2012] | |
RS-WBPM-EVI | 0.82/0.96 | 2005 | In situ | ERA-Interim | Day/month | This study | |
GLEAM | 0.72/0.85 | 2005 | In situ | LPRM, CMORPH, NSIDC | Day/month | Miralles et al. [2011] | |
RS-WBPM-EVI | 0.88 | 2002–2006 | In situ | In situ | Month | This study | |
CONUS-PT (PFT-
![]() |
0.77 | 2001–2006 | In situ | In situ | Month | Jin et al. [2011] | |
PT-JPL | 0.83 | 2000–2003 | In situ | In situ | Month | Fisher et al. [2008] | |
US-Var | RS-WBPM-EVI | 0.86 | 2001–2006 | In situ | In situ | Day | This study |
ARTS E | 0.56 | 2001–2005 | In situ | In situ | Day | Yan et al. [2012] | |
RS-WBPM-EVI | 0.93 | 2001–2006 | In situ | In situ | Month | This study | |
CONUS-PT (PFT-
![]() |
0.61 | 2001–2006 | In situ | In situ | Month | Jin et al. [2011] | |
PT-JPL | 0.81 | 2000–2003 | In situ | In situ | Month | Fisher et al. [2008] | |
US-Blo | RS-WBPM-EVI | 0.88 | 2001–2006 | In situ | In situ | Month | This study |
CONUS-PT (PFT-
![]() |
0.81 | 2001–2006 | In situ | In situ | Month | Jin et al. [2011] | |
US-Me2 | RS-WBPM-EVI | 0.58 | 2005–2007 | In situ | In situ | Day | This study |
ARTS E | 0.60 | 2005–2007 | In situ | In situ | Day | Yan et al. [2012] | |
RS-WBPM-EVI | 0.76 | 2002–2006 | In situ | In situ | Month | This study | |
CONUS-PT (PFT-
![]() |
0.77 | 2001–2006 | In situ | In situ | Month | Jin et al. [2011] | |
PT-Mi2 | RS-WBPM-EVI | 0.59 | 2005–2006 | SRB | ERA-Interim | Day | This study |
GLEAM | 0.56 | 2005–2007 | SRB | ERA-Interim, CMORPH, ESA | Day | Michel et al. [2016] | |
MOD16 | 0.43 | 2005–2007 | SRB | ERA-Interim, CMORPH, ESA | Day | Michel et al. [2016] | |
RS-WBPM-EVI | 0.50/0.70 | 2005 | In situ | ERA-Interim | Day/month | This study | |
GLEAM | 0.41/0.62 | 2005 | In situ | LPRM, CMORPH, NSIDC | Day/month | Miralles et al. [2011] | |
ES-LMa | RS-WBPM-EVI | 0.45 | 2005 | In situ | ERA-Interim | Day | This study |
GLEAM | 0.56 | 2005 | In situ | LPRM, CMORPH, NSIDC | Day | Miralles et al. [2011] | |
RS-WBPM-EVI | 0.86 | 2005 | In situ | ERA-Interim | Month | This study | |
GLEAM | 0.85 | 2005 | In situ | LPRM, CMORPH, NSIDC | Month | Miralles et al. [2011] | |
IT-Noe | RS-WBPM-NDVI | 0.37 | 2005–2007 | SRB | ERA-Interim | Day | This study |
GLEAM | 0.17 | 2005–2007 | SRB | ERA-Interim, CMORPH, ESA | Day | Michel et al. [2016] | |
MOD16 | 0.001 | 2005–2007 | SRB | ERA-Interim | Day | Michel et al. [2016] | |
PT-JPL | 0.05 | 2005–2007 | SRB | ERA-Interim | Day | Michel et al. [2016] |
- a Results of MOD16 at IT-Noe are also presented. Data on a monthly scale are shown with a gray background.
On a daily scale, RS-WBPM yields higher
at US-Ton, PT-Mi2, and IT-Noe sites, but lower
than GLEAM at ES-LMa site. On a monthly scale, RS-WBPM also yields higher
at US-Ton and PT-Mi2 sites, and comparable
at ES-LMa site. Compared with the
of RS-WBPM driven by in situ meteorological data, that of RS-WBPM driven by the ERA-Interim meteorological data undergoes a significant fall at ES-LMa site. We found that descending values of
were primarily caused by uncertainties in input precipitation. After substituting the ERA-Interim precipitation for the in situ value, RS-WBPM yielded
of 0.53 for daily
and 0.92 for monthly
at ES-LMa. Simulation of RS-WBPM in arid and semiarid regions highly depends on the input water source. Descending values of
for daily
at ES-LMa demonstrates that uncertainties of input precipitation will significantly affect RS-WBPM's estimation of daily soil water content, and therefore daily
. To correct the mismatch between simulated soil water content and the in situ value on a daily scale, the microwave-retrieved soil moisture data were assimilated with the modeled value in GLEAM. This strategy could help reduce the error of simulated soil moisture on a daily scale to some extent [Miralles et al., 2011]. However, the assimilation may also introduce uncertainties of satellite-retrieved data to the modeled value. In this study, we do not incorporate the microwave-retrieved soil moisture; however, the comparable performance of RS-WBPM with GLEAM at ES-LMa site on a monthly scale demonstrates that the uncertainties in daily precipitation could be smoothed by increasing the temporal scale. This result, and the better performance of RS-WBPM at the other three sites (US-Ton, PT-Mi2, and IT-Noe), implies that equations 7-23, which include vertical root distribution information, could more accurately estimate the water stress factor in the AMC.
The RS-WBPM model yields comparable
to that of the ARTS E model [Yan et al., 2012] at US-Ton and US-Me2 sites, but significantly higher
at US-Var, which demonstrates the significance of including vertical root distribution information. The shallowest soil layer (0–10 cm) severely lacks water in the summer season at US-Var, and the grass has a very shallow root system. Water in depth is unable to supplement the water demand of the grassland, but the water stress factor of the entire soil profile estimated by ARTS E may fail to reflect this information. The model of Jin et al. [2011] (CONUS-PT) is useful, in which an empirical equation incorporating soil moisture and LAI is proposed to calculate the PT coefficient,
, and soil moisture is derived from a water balance model. This method performs well with site-based optimum,
, but when the model is parameterized by plant-functional-type-based coefficients (PFT-
),
decreased by 0.25 (from 0.86 to 0.61), 0.12 (from 0.89 to 0.77), and 0.07 (from 0.88 to 0.81) at the US-Var, US-Ton, and US-Blo sites, respectively (result of the model with optimum
is not shown in Table 5). RS-WBPM-EVI shows a comparable result to CONUS-PT with site-based optimum
, and therefore the site-based coefficients of CONUS-PT may reflect the real water stress condition at a specific site. However, only the value of
averaged by the biome type was available in their model on regional and continental scales.
The PT-JPL model and MOD16 [Fisher et al., 2008; Mu et al., 2011; Michel et al., 2016] are also compared with RS-WBPM. Both PT-JPL and MOD16 use VPD instead of soil water information to estimate water stress for the evapotranspiration source. PT-JPL yields comparable
with the models incorporating a soil water balance model at US-Ton and US-Var. However, compared with the RS-WBPM and GLEAM models, this model and the MOD16 model yield significantly lower values of
at the IT-Noe site. The result indicates that VPD is capable of reflecting water stress of the evapotranspiration source, but it is less reliable than simulated soil water information.
4.2 Limitations of Using VIs to Parameterize

Although VIs are useful in parameterizing
[Yebra et al., 2013], it has definite limitations. Olsen et al. [2015] demonstrated that satellite-retrieved VI is capable of reflecting the spatial variation of water stress in dry regions. Approaches to evapotranspiration simulations based on the
space method have used satellite-retrieved VI (NDVI) and temperature information to calculate the surface water stress condition [Jiang and Islam, 2001; Wang et al., 2006; Tang et al., 2010]. However,
resulting from a directly regressed equation using NDVI or EVI does not adequately reflect the temporal variation of water stress, especially for biomes that root shallowly in the AMC. The
of EBF, GRA, SHR, and SAV was significantly overestimated by the Ye-VI algorithm in the dry season.
Another limitation of the cross-calibrated
algorithm is that it does not estimate the differences between magnitudes of
in differing biomes. The
algorithms of Yebra et al. [2013] were cross-calibrated using observed data of various biomes. This calibration assumes that different biomes with the same VI value (EVI or NDVI) have the same
value at a pixel scale, it may be inappropriate on a global scale. The parameterization of
is important to RS-WBPM, because the estimation of evapotranspiration on the surface during the wet season (when the surface is not stressed by water deficit) relies on
. Therefore, a simple correction factor,
(see equation 4), is used to scale the result of equation 3. As the
of EBF in the AMC was significantly overestimated by equation 3. The estimations of
by Ye-EVI with
and
during the wet season (January–April, November–December) at six EBF sites (FR-Pue, IT-Cpz, IT-Cp2, IT-Lec, PT-Esp, and PT-Mi1) are presented in Figure 9, where
means that the value of
is calculated using equation 3 without correction with
. The mean value of the simulated daily water stress factor during the wet season by RS-WBPM-EVI at the six EBF sites was approximately 0.95, which implies that the surface was well-watered during the wet season. Figure 9 shows that Ye-EVI with
and
yields the same
; however, Ye-EVI with
yields lower RMSE, while the Ye-EVI with
significantly overestimates
. This implies the necessity of correcting to
. However, using
to scale
is not the optimum method, as Figure 9b shows that the slope of the fitted line is relatively low. Therefore, future work is necessary to calibrate
using VI based on the plant functional type (PFT), as it is anticipated that this would help improve the RS-WBPM model.

Scatterplots of observed daily
in the wet season at six EBF sites (FR-Pue, IT-Cpz, IT-Cp2, IT-Lec, PT-Esp, and PT-Mi1) versus estimations by Ye-EVI with (a)
= 1 and (b)
= 0.4.
4.3 Soil Water Content Simulation
RS-WBPM outputs the estimated actual latent heat flux and the soil water content of different soil layers. The output soil water content at the shallowest soil layer (0–10 cm) was compared with the in situ value (Table 6). This validation aims to reflect the effectiveness of RS-WBPM in simulating soil water content under a Mediterranean climate. Simulated soil water in the shallowest layer was validated for two reasons: (a) a considerable proportion (approximately 18–44%) of the fine root biomass of plants is distributed in this layer; (b) the shallowest soil layer has a faster dynamic than the other layers [Miralles et al., 2011]; it was thus considered that validation could demonstrate the model's efficiency in simulating soil water. The in situ values were retrieved from observations at the flux sites available in this study. Among the 27 flux sites used in this study, 23 sites provide available long-term daily soil water volumetric content observations in the shallowest soil layer; the depths of the shallowest soil layers where the soil water volumetric content were measured at the 23 sites varied between 4 and 30 cm (Table 6).
Site | Biome | Period | Size of Available Observations | Measurement Depth | R1 | R2 | ||
---|---|---|---|---|---|---|---|---|
RS-WBPM-EVI | RS-WBPM-NDVI | RS-WBPM-EVI | RS-WBPM-NDVI | |||||
IT-BCib | CRO | 2004–2006 | 771 | 0–20/5 cm | 0.51 | 0.49 | 0.56 | 0.53 |
IT-CA1 | DBF | 2011–2014 | 1282 | 0–5 cm | 0.64 | 0.63 | 0.56 | 0.54 |
IT-CA3b | DBF | 2011–2013 | 698 | 0–15/5 cm | 0.90 | 0.89 | 0.86 | 0.85 |
IT-Col | DBF | 2004–2006 | 602 | 0–30 cm | 0.80 | 0.82 | 0.81 | 0.82 |
IT-Ro1 | DBF | 2000–2006 | 2346 | 0–10 cm | 0.76 | 0.77 | 0.74 | 0.76 |
IT-Ro2 | DBF | 2002–2006 | 1012 | 0–7 cm | 0.55 | 0.56 | 0.60 | 0.61 |
IT-Cp2 | EBF | 2012–2014 | 808 | 0–10 cm | 0.25 | 0.25 | 0.25 | 0.26 |
IT-Cpz | EBF | 2000–2006 | 1909 | 0–20 cm | 0.76 | 0.78 | 0.78 | 0.80 |
IT-Lec | EBF | 2005–2006 | 464 | 0.83 | 0.88 | 0.81 | 0.84 | |
ES-ES1 | ENF | 2000–2005 | 1663 | 0–20 cm | 0.53 | 0.52 | 0.50 | 0.51 |
IT-SRo | ENF | 2002–2006 | 1731 | 0–5 cm | 0.62 | 0.59 | 0.65 | 0.71 |
US-Blo | ENF | 2000–2006 | 2491 | 0–10 cm | 0.90 | 0.91 | 0.94 | 0.94 |
US-Me2 | ENF | 2002–2014 | 4712 | 0–30 cm | 0.70 | 0.73 | 0.70 | 0.73 |
US-Me4 | ENF | 2000 | 366 | 0–20 cm | 0.70 | 0.70 | 0.63 | 0.64 |
US-Me6 | ENF | 2010–2014 | 1636 | 0–10 cm | 0.79 | 0.81 | 0.72 | 0.72 |
IT-CA2b | GRA | 2011–2013 | 726 | 0–15/5 cm | 0.63 | 0.62 | 0.58 | 0.54 |
PT-Mi2 | GRA | 2004–2006 | 773 | 0–15 cm | 0.87 | 0.83 | 0.89 | 0.86 |
US-Var | GRA | 2001–2006 | 2159 | 0–10 cm | 0.92 | 0.91 | 0.91 | 0.91 |
ES-LgS | SHR | 2007–2008 | 372 | 0–4 cm | 0.89 | 0.87 | 0.85 | 0.84 |
ES-LJu | SHR | 2004–2013 | 2963 | 0–15 cm | 0.85 | 0.81 | 0.83 | 0.82 |
IT-Noe | SHR | 2004–2014 | 3863 | 0–20 cm | 0.77 | 0.76 | 0.76 | 0.75 |
ES-LMa | SAV | 2004–2006 | 844 | 0–5 cm | 0.90 | 0.89 | 0.91 | 0.88 |
US-Ton | SAV | 2001–2006 | 2095 | 0–20 cm | 0.86 | 0.85 | 0.86 | 0.85 |
Mean | 0.74 | 0.73 | 0.73 | 0.73 |
- a R1: results driven by site observed meteorological data; R2: results driven by ERA-Interim meteorological data (including surface radiation).
- b Depths of shallowest soil layer (where SWC was measured at IT-BCi, IT-CA2, and IT-CA3 sites) were varied throughout the measurement period. Depths of the shallowest layer were 20 cm at IT-BCi prior to 16 November 2005; 15 cm at IT-CA2 prior to 27 June 2012; and 15 cm at IT-CA3 prior to 3 April 2012; after which dates the depth at all three sites was changed to 5 cm.
Results showed that RS-WBPM simulated well the variation in water content in the shallowest soil layer. RS-WBPM-EVI and RS-WBPM-NDVI yielded mean correlations of 0.74 and 0.73, respectively, using in situ meteorological data at the 23 sites. Correlations (R2) resulting from ERA-Interim meteorological data were comparable with those from in situ data. RS-WBPM-EVI and RS-WBPM-NDVI both yielded R1 values higher than 0.6 at 19 sites, and yielded R2 values higher than 0.6 at 17 and 18 sites, respectively. The mean value of R2 was higher than that of GLEAM simulating the soil water content of the shallowest 5 cm soil layer at 43 SCAN study sites [Miralles et al., 2011]. The results therefore imply that the soil water balance strategy used in this study (see section 2.1.3) is advanced.
4.4 Uncertainties of Soil Properties
The simulation of RS-WBPM highly depends on the soil properties input. Soil properties from each of the sites used in this study were retrieved from the IGBP data set with a spatial resolution of 0.0625 arc degree. The soil water stress factor simulated by the water balance module of RS-WBPM for each layer depends on the inflow water and the water holding capacity (
) of the soil, which is the difference between wilting point (
) and field capacity (
). As errors of
or
will introduce errors to
, uncertainties will be introduced to the output soil water content and therefore the estimated evapotranspiration. The water balances of each soil layer are not independent from each other, and thus the errors of
will not linearly effect the outputs of the model. However, it is necessary to explore how the result of RS-WBPM responds to the error in
.
We therefore reran the RS-WBPM model using in situ meteorological data and
with perturbations; anomalies of
and RMSE of RS-WBPM-EVI model incorporating
with perturbations are presented (Figure 10) and perturbations of
are specified as [−25, 25%], with a variation step of 5%.

Response of (a)
and (b) RMSE of RS-WBPM-EVI simulating
to errors of soil water holding capacity (
) at 27 flux sites. Red solid line represents mean fluctuations at all sites.
Results show that overall RS-WBPM is not very sensitive to the error of
, as shown by the lines of mean anomalies of
(Figure 10a) and RMSE (Figure 10b), which do not fluctuate significantly with variation in
errors. The results also show that the anomalies of
and RMSE strengthen with an increase in the absolute values of the relative errors.
(RMSE) of RS-WBPM incorporating
with perturbations of −25% has the strongest anomalies, −0.094 to 0.022 (−3.34 to 4.31
). However, the anomalies of
(RMSE) of RS-WBPM with
with
perturbations fluctuate between −0.048 and 0.028 (−0.92 and
), and the anomaly intensity of
(RMSE) decreases with the error. This analysis indicates that if the relative error of
at the soil profile is controlled within [−15, 15%] then the performances of RS-WBPM will not fluctuate significantly. This result is therefore encouraging for the large-scale application of RS-WBPM.
5 Conclusion
Recent studies have shown the failure of older version PM-based models (PMOV) to satisfactorily simulate water stress on a canopy or a bulk surface when estimating ET in the AMC [Mu et al., 2007, 2011; Vinukollu et al., 2011]. To verify this phenomenon in this study, four older PM-based models were evaluated using the observed data at 27 flux sites in the AMC. Meanwhile, a new PM-based model, RS-WBPM incorporating a novel approach to reflecting the water stress on ET, was developed to address the issue and to more accurately estimate ET in the AMC. In this new approach, a multilayer water balance module was employed to simulate the surface's WSF, which is the weighted sum of simulated SWSF of each soil layer. In this respect, the weight of each soil layer was determined by the proportion of fine root biomass in the current layer and that in the wettest layer. The fine root biomass proportion in the soil layer is the weighted sum of the fine root biomass proportion of the overstory species, understory species and bare soil, and the weight of each surface component is its fractional cover at a pixel scale.
The evaluation of the four older PM-based models showed that these models failed to estimate the magnitude and variation of ET at most sites located in the AMC during summer when severe water stress occurred. Conversely, the developed RS-WBPM model was successful and outperformed the older PM-based models when simulating the daily
for most biome types. The improvement in the RS-WBPM model was most apparent when simulating the
for EBF, SHR, SAV, and GRA. Results show that RS-WBPM-EVI generally yields better results than RS-WBPM-NDVI, but RS-WBPM-NDVI performs better than RS-WBPM-EVI for SHR. The use of RS-WBPM-NDVI is therefore recommended for SHR, and RS-WBPM-EVI is recommended for CRO, DBF, EBF, ENF, GRA, and SAV. With recommended parameterizations, RS-WBPM yielded
(RMSE = 18.72
) for all 27 sites, but its performances were no better than Ye-EVI for CRO because of a lack of irrigation information; thus, Ye-EVI is recommended for irrigated CRO land when irrigation information is not available.
A further comparison between RS-WBPM and other ET models incorporating a water balance model or using VPD to reflect water stress revealed the following two points: (a) RS-WBPM better simulates soil moisture and evapotranspiration in the AMC than other models that do not incorporate information about the mutual effects of VRD and SWC; (b) simulated soil water information is more reliable in reflecting water stress on the surface than VPD. The limitations of using VIs to parameterize
was also addressed in this study, and it is considered that a biome-based correction factor
could help the RS-WBPM more accurately simulate
; however, the correction is still inadequate and future work on this issue is necessary. In addition, the water stress factor of RS-WBPM relies on inflow water and the water holding capacity (
), but it was found that errors of
within the perturbations of [−15, 15%] would not significantly influence the result of RS-WBPM.
These results indicate that the RS-WBPM is reliable for simulating
under a Mediterranean climate and that it has great potential for implementation on a regional and global scale, because all inputs, vegetation indices, soil parameters, vegetation cover information, and meteorological parameters of RS-WBPM can be retrieved from globally available data sets.
Acknowledgments
We would like to express our great appreciation to the Editor of JAMES and two anonymous reviewers as their contributions have considerably improved this paper. Thanks to language editors of “Enago China” for their efforts on improving the language of this manuscript. Many thanks to Yan Hao of National Meteorological Center, China Meteorological Administration and Long Di of Tsinghua University as they have given me suggestions on improving this study. Thanks to Arnaud Carrara of CEAM (Centro de Estudios Ambientales del Mediterráneo) for his suggestions on data usage and improving this study. Thanks to Dario Papale and Simone Sabbatini of University of Tuscia (the PI of IT-CA1, IT-CA2, and IT-CA3 site) and Paul Di Tommasi of CNR-ISAFOM (PI of IT-BCi site) for providing me essential information of their flux sites. This study is supported by The National Natural Science Foundation of China (No. 31571565, 31671585), National Key Research and Development Program of China (2016YFD0300101), and CAS-Xinjiang Region Cooperation Project (Y42301101A), the Hundred Talents Program of the Chinese Academy of Sciences (Y24002101A), the CAS-TWAS Project of Drought Monitoring in Asia (Y3YI2701KB), and the CAS-RADI 1-3-5 Innovation Project (Y3ZZ15101A). The soil properties used in this study was retrieved from IGBP-DIS data set (https://daac.ornl.gov/cgi-bin/dsviewer.pl?ds_id=569). The LAI data at all the flux sites used in this study was retrieved from the MODIS subset of MOD15A2 of Field Site and Flux tower (http://daac.ornl.gov/cgi-bin/MODIS/GR_col5_1/mod_viz.html). The NDVI and EVI data for ES-LgS, IT-CA1, IT-CA3, IT-Cp2, and US-Me6 sites were retrieved from the flux subsets of MOD13Q1 using the Python client of MODIS Web Service (http://daac.ornl.gov/MODIS/MODIS-menu/modis_webservice.html), and that for the rest sites were from the MODIS subset of MOD13Q1 and MYD13Q1 of Field Site and Flux tower (http://daac.ornl.gov/cgi-bin/MODIS/GR_col5_1/mod_viz.html). The meteorological data used for gap-filling is retrieved from ERA-Interim (http://apps.ecmwf.int/datasets/data/interim-full-daily/levtype=sfc/). The canopy height information at ES-ES2 sites was retrieved from Global forest canopy height data developed using Geoscience Laser Altimeter System (GLAS) aboard ICESat by Simard et al. [2011], this data set is available on http://lidarradar.jpl.nasa.gov/. The eddy covariance data used in this study was retrieved from FLUXNET LaThuile Dataset 2007 and FLUXNET2015 Dataset, both are available on http://fluxnet.fluxdata.org/. The FLUXNET LaThuile Dataset 2007 is acquired by the FLUXNET community and in particular by the following networks: AmeriFlux (U.S. Department of Energy, Biological and Environmental Research, Terrestrial Carbon Program (DE-FG02-04ER63917 and DE-FG02-04ER63911)), AfriFlux, AsiaFlux, CarboAfrica, CarboEuropeIP, CarboItaly, CarboMont, ChinaFlux, Fluxnet-Canada (supported by CFCAS, NSERC, BIOCAP, Environment Canada, and NRCan), GreenGrass, KoFlux, LBA, NECC, OzFlux, TCOS-Siberia, USCCC. We acknowledge the financial support to the eddy covariance data harmonization provided by CarboEuropeIP, FAO-GTOS-TCO, iLEAPS, Max Planck Institute for Biogeochemistry, National Science Foundation, University of Tuscia, Université Laval and Environment Canada and US Department of Energy and the database development and technical support from Berkeley Water Center, Lawrence Berkeley National Laboratory, Microsoft Research Science, Oak Ridge National Laboratory, University of California-Berkeley, University of Virginia. And FLUXNET 2015 data set is acquired and shared by the FLUXNET community, including these networks: AmeriFlux, AfriFlux, AsiaFlux, CarboAfrica, CarboEuropeIP, CarboItaly, CarboMont, ChinaFlux, Fluxnet-Canada, GreenGrass, ICOS, KoFlux, LBA, NECC, OzFlux-TERN, TCOS-Siberia, and USCCC. The FLUXNET eddy covariance data processing and harmonization was carried out by the ICOS Ecosystem Thematic Center, AmeriFlux Management Project and Fluxdata project of FLUXNET, with the support of CDIAC, and the OzFlux, ChinaFlux, and AsiaFlux offices.