Volume 9, Issue 1 p. 168-192
Research Article
Open Access

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

Yun Bai

Yun Bai

Key Laboratory of Digital Earth Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing, China

University of Chinese Academy of Sciences, Beijing, China

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Jiahua Zhang

Corresponding Author

Jiahua Zhang

Key Laboratory of Digital Earth Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing, China

Correspondence to: J. Zhang, [email protected]; F. Yao, [email protected]Search for more papers by this author
Sha Zhang

Sha Zhang

Key Laboratory of Digital Earth Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing, China

University of Chinese Academy of Sciences, Beijing, China

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Upama Ashish Koju

Upama Ashish Koju

Key Laboratory of Digital Earth Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing, China

University of Chinese Academy of Sciences, Beijing, China

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Fengmei Yao

Fengmei Yao

University of Chinese Academy of Sciences, Beijing, China

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Tertsea Igbawua

Tertsea Igbawua

Key Laboratory of Digital Earth Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing, China

University of Chinese Academy of Sciences, Beijing, China

University of Agriculture, Makurdi, Nigeria

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First published: 04 January 2017
Citations: 39

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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0001 ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0002 18.72 urn:x-wiley:19422466:media:jame20358:jame20358-math-0003) for all 27 sites and urn:x-wiley:19422466:media:jame20358:jame20358-math-0004 ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0005 18.21 urn:x-wiley:19422466:media:jame20358:jame20358-math-0006) for 25 nonagricultural sites. However, combined results from the optimum older PM-based models at specific sites show urn:x-wiley:19422466:media:jame20358:jame20358-math-0007 ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0008 20.74 urn:x-wiley:19422466:media:jame20358:jame20358-math-0009) 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0010 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0011 of land ET accounted for transpiration [Schlesinger and Jasechko, 2014] on a global scale. Understanding the distribution of urn:x-wiley:19422466:media:jame20358:jame20358-math-0012 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0013 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 ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0014). 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0015 is nearly 0. However, studies have shown significant seasonal variations in urn:x-wiley:19422466:media:jame20358:jame20358-math-0016 [Ma et al., 2015; Zhang et al., 2016]; for example, an approximate value of urn:x-wiley:19422466:media:jame20358:jame20358-math-0017 = 0.5 was observed during the rainy season for the highest alpine steppe [Ma et al., 2015], and an annual value of urn:x-wiley:19422466:media:jame20358:jame20358-math-0018 = 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].

Therefore, the PM-based model with a clear physical mechanism is more useful. For application on a regional and global scales, the RS-based PM (RS-PM) model was suggested by Cleugh et al. [2007]
urn:x-wiley:19422466:media:jame20358:jame20358-math-0019(1)
where urn:x-wiley:19422466:media:jame20358:jame20358-math-0020 is the latent heat of evaporation ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0021), urn:x-wiley:19422466:media:jame20358:jame20358-math-0022 is the evapotranspiration rate ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0023), urn:x-wiley:19422466:media:jame20358:jame20358-math-0024 is the gradient of the saturated vapor pressure to the air temperature ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0025), urn:x-wiley:19422466:media:jame20358:jame20358-math-0026 is the psychrometric constant ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0027), urn:x-wiley:19422466:media:jame20358:jame20358-math-0028 is the available energy for the bulk surface ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0029), urn:x-wiley:19422466:media:jame20358:jame20358-math-0030 is the air density ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0031), urn:x-wiley:19422466:media:jame20358:jame20358-math-0032 is the specific heat of air at a constant pressure ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0033), urn:x-wiley:19422466:media:jame20358:jame20358-math-0034 is the vapor pressure deficit ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0035), urn:x-wiley:19422466:media:jame20358:jame20358-math-0036 is the aerodynamic conductance ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0037), and urn:x-wiley:19422466:media:jame20358:jame20358-math-0038 is the surface conductance ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0039).

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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0040 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

Surface conductance plays a key role in PM-based models estimating ET [Yan et al., 2012]. Jarvis [1976] presented an equation to explain the complex effect of the environment on the stomatal conductance, which is
urn:x-wiley:19422466:media:jame20358:jame20358-math-0041(2)
where urn:x-wiley:19422466:media:jame20358:jame20358-math-0042 is the canopy conductance, urn:x-wiley:19422466:media:jame20358:jame20358-math-0043 is the maximum value of the canopy conductance for a certain region, and urn:x-wiley:19422466:media:jame20358:jame20358-math-0044 is a function of the constraint factor urn:x-wiley:19422466:media:jame20358:jame20358-math-0045, among these variables, urn:x-wiley:19422466:media:jame20358:jame20358-math-0046 denotes the air temperature, urn:x-wiley:19422466:media:jame20358:jame20358-math-0047 denotes the vapor pressure deficit, urn:x-wiley:19422466:media:jame20358:jame20358-math-0048 denotes the solar radiation density, urn:x-wiley:19422466:media:jame20358:jame20358-math-0049 denotes the carbon dioxide density, and urn:x-wiley:19422466:media:jame20358:jame20358-math-0050 denotes the leaf water potential. Among these factors, urn:x-wiley:19422466:media:jame20358:jame20358-math-0051 which accounts for the water stress condition of plants is critically important for dry climate. Some widely used PM-based models only use VPD to reflect water stress for transpiration [Mu et al., 2007; Leuning et al., 2008; Zhang et al., 2010; Mu et al., 2011], but the effectiveness of VPD is questionable in reflecting the water condition of the surface.

However, as it is difficult in practice to obtain global temporal-continuous urn:x-wiley:19422466:media:jame20358:jame20358-math-0052 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.

Details are in the caption following the image

Flow chart of multilayer water balance module, where subscript t denotes index of period, superscript urn:x-wiley:19422466:media:jame20358:jame20358-math-0053 denotes soil layer index, urn:x-wiley:19422466:media:jame20358:jame20358-math-0054 and urn:x-wiley:19422466:media:jame20358:jame20358-math-0055 represent soil water content and soil water content change, respectively, urn:x-wiley:19422466:media:jame20358:jame20358-math-0056 is the soil water stress factor, urn:x-wiley:19422466:media:jame20358:jame20358-math-0057 is the water stress factor for surface evapotranspiration, urn:x-wiley:19422466:media:jame20358:jame20358-math-0058 is the weight of the soil layer, urn:x-wiley:19422466:media:jame20358:jame20358-math-0059 is the inflow water source, and urn:x-wiley:19422466:media:jame20358:jame20358-math-0060 is estimated actual evapotranspiration. The symbol without superscript urn:x-wiley:19422466:media:jame20358:jame20358-math-0061 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

We adopt the one-source RS-PM model proposed by Cleugh et al. [2007] in this study (equation 1). The original version of the surface conductance algorithm in this model was parameterized with LAI and calibrated using two flux sites in Australia. Models of the urn:x-wiley:19422466:media:jame20358:jame20358-math-0062 parameterized using RS data, such as vegetation indices (VI), have been suggested [Yebra et al., 2013]. We used the simple model developed by Yebra et al. [2013] that only involves VI to calculate urn:x-wiley:19422466:media:jame20358:jame20358-math-0063 and it was calibrated globally.
urn:x-wiley:19422466:media:jame20358:jame20358-math-0064(3)
where urn:x-wiley:19422466:media:jame20358:jame20358-math-0065 is the surface conductance, VI is the vegetation index, urn:x-wiley:19422466:media:jame20358:jame20358-math-0066 is the minimum value of VI indicating the VI value of the bare soil, and urn:x-wiley:19422466:media:jame20358:jame20358-math-0067 and urn:x-wiley:19422466:media:jame20358:jame20358-math-0068 are regression coefficients.

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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0069 for rain-free days ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0070), and EVI is recommended for evergreen needle leaf forests (ENF). However, urn:x-wiley:19422466:media:jame20358:jame20358-math-0071 parameterized with NDVI ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0072) 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0073 or RMSE between models parameterized with NDVI and Kc. In addition, the model parameterized with EVI yielded higher urn:x-wiley:19422466:media:jame20358:jame20358-math-0074 than that with NDVI or Kc. For NDVI, the coefficients of equation 3 are specified as urn:x-wiley:19422466:media:jame20358:jame20358-math-0075 = 0.002 urn:x-wiley:19422466:media:jame20358:jame20358-math-0076, urn:x-wiley:19422466:media:jame20358:jame20358-math-0077 = 4.11, and urn:x-wiley:19422466:media:jame20358:jame20358-math-0078= 0.4; and for EVI, the coefficients are urn:x-wiley:19422466:media:jame20358:jame20358-math-0079 = 0.0025 urn:x-wiley:19422466:media:jame20358:jame20358-math-0080, urn:x-wiley:19422466:media:jame20358:jame20358-math-0081 = 3.15, and urn:x-wiley:19422466:media:jame20358:jame20358-math-0082= 0.1.

Specially, the coefficients of the urn:x-wiley:19422466:media:jame20358:jame20358-math-0083 equation were cross-calibrated for all biomes. However, the equation with the same input VI value (either NDVI or EVI) results in the same urn:x-wiley:19422466:media:jame20358:jame20358-math-0084 value for all the biomes, which is not appropriate on a global scale. To ameliorate this problem, we make a simple correction to urn:x-wiley:19422466:media:jame20358:jame20358-math-0085 as follows:
urn:x-wiley:19422466:media:jame20358:jame20358-math-0086(4)
where urn:x-wiley:19422466:media:jame20358:jame20358-math-0087 is the factor used to correct urn:x-wiley:19422466:media:jame20358:jame20358-math-0088, which is specified in Table 1.
Table 1. urn:x-wiley:19422466:media:jame20358:jame20358-math-0089 for Biomes of CRO, EBF, ENF, DBF, GRA, SHR, and SAVa
urn:x-wiley:19422466:media:jame20358:jame20358-math-0090b GRO EBF ENF DBF GRA SHR SAV
urn:x-wiley:19422466:media:jame20358:jame20358-math-0091 1.5 0.4 1 0.55 1 1 1
urn:x-wiley:19422466:media:jame20358:jame20358-math-0092 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0093 denotes urn:x-wiley:19422466:media:jame20358:jame20358-math-0094 parameterized with EVI and urn:x-wiley:19422466:media:jame20358:jame20358-math-0095 denotes urn:x-wiley:19422466:media:jame20358:jame20358-math-0096 parameterized with NDVI.
NDVI and other VIs are capable of indicating water stress in dry regions [Olsen et al., 2015]; however, they may not work in the AMC because of inconsistent seasonal variations between VIs and water stress [Maselli et al., 2014a, 2014b]. Therefore, correcting urn:x-wiley:19422466:media:jame20358:jame20358-math-0097 using WSF is essential. The actual ET ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0098) is calculated as follows:
urn:x-wiley:19422466:media:jame20358:jame20358-math-0099(5)

Here urn:x-wiley:19422466:media:jame20358:jame20358-math-0100 is the actual water stress factor for a certain region during a specific period and urn:x-wiley:19422466:media:jame20358:jame20358-math-0101 is the surface conductance scaled by urn:x-wiley:19422466:media:jame20358:jame20358-math-0102

2.1.2 Incorporating Vertical Root Distribution Information to Calculate Water Stress Factor

The studies of Zhang et al. [2015] and Shi et al. [2015] imply that the vertical distribution of a root has a significant impact on the water stress condition of a plant. The water stress of plants is determined by variations in both water content and root density along the vertical soil profile. Zhang et al. [2015] suggested calculating the WSF for plants as follows:
urn:x-wiley:19422466:media:jame20358:jame20358-math-0103(6)
where urn:x-wiley:19422466:media:jame20358:jame20358-math-0104 is the water stress factor incorporating vertical root distribution information, urn:x-wiley:19422466:media:jame20358:jame20358-math-0105 is the normalized root length density at soil depth z, urn:x-wiley:19422466:media:jame20358:jame20358-math-0106 is the water stress factor (0–1) at soil depth urn:x-wiley:19422466:media:jame20358:jame20358-math-0107. Compared with other methods that do not incorporate vertical root distribution information, this method shows a significant improvement in estimating the stomatal conductance of winter wheat. However, in the ET model GLEAM, the WSF of the surface is determined by the wettest soil layer. The model also performs well for arid and semiarid regions [Miralles et al., 2011; Michel et al., 2016].
This therefore implies two assumptions: (a) the water stress condition of a plant is significantly affected by VRD information and (b) the wettest soil layer has a stronger effect than the other layers on surface evapotranspiration. To calculate WSF in this study, we therefore incorporate both of these assumptions, and the method used to calculate WSF is proposed as follows.
  1. 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, urn:x-wiley:19422466:media:jame20358:jame20358-math-0108. (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:

    urn:x-wiley:19422466:media:jame20358:jame20358-math-0109(7)
    urn:x-wiley:19422466:media:jame20358:jame20358-math-0110(8)
    urn:x-wiley:19422466:media:jame20358:jame20358-math-0111(9)
    urn:x-wiley:19422466:media:jame20358:jame20358-math-0112(10)
    urn:x-wiley:19422466:media:jame20358:jame20358-math-0113(11)
    where superscript urn:x-wiley:19422466:media:jame20358:jame20358-math-0114 denotes the soil layer index, subscript urn:x-wiley:19422466:media:jame20358:jame20358-math-0115 denotes the index of the period, urn:x-wiley:19422466:media:jame20358:jame20358-math-0116 represents the water stress factor for evapotranspiration, and urn:x-wiley:19422466:media:jame20358:jame20358-math-0117 represents the soil water stress factor of soil layer urn:x-wiley:19422466:media:jame20358:jame20358-math-0118 during period urn:x-wiley:19422466:media:jame20358:jame20358-math-0119. Furthermore, urn:x-wiley:19422466:media:jame20358:jame20358-math-0120 and urn:x-wiley:19422466:media:jame20358:jame20358-math-0121 denote the input water source (mm) and maximum evapotranspiration rate (mm) during period urn:x-wiley:19422466:media:jame20358:jame20358-math-0122 is estimated using equations 1 and 4; urn:x-wiley:19422466:media:jame20358:jame20358-math-0123, urn:x-wiley:19422466:media:jame20358:jame20358-math-0124, urn:x-wiley:19422466:media:jame20358:jame20358-math-0125, and urn:x-wiley:19422466:media:jame20358:jame20358-math-0126 are precipitation (mm), rainfall (mm), snowmelt (mm), and snow depth (water equivalent: mm) during period urn:x-wiley:19422466:media:jame20358:jame20358-math-0127; urn:x-wiley:19422466:media:jame20358:jame20358-math-0128 is the air temperature near the surface ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0129); urn:x-wiley:19422466:media:jame20358:jame20358-math-0130 is the water content of soil layer urn:x-wiley:19422466:media:jame20358:jame20358-math-0131 during period urn:x-wiley:19422466:media:jame20358:jame20358-math-0132 and is the result of the soil water balance of soil layer urn:x-wiley:19422466:media:jame20358:jame20358-math-0133 during the last period; urn:x-wiley:19422466:media:jame20358:jame20358-math-0134 is the wilting point (mm) of soil layer urn:x-wiley:19422466:media:jame20358:jame20358-math-0135. urn:x-wiley:19422466:media:jame20358:jame20358-math-0136 is the critical value of the soil water content when stomatal conductance is at its maximum [Raab et al., 2015] and is set as urn:x-wiley:19422466:media:jame20358:jame20358-math-0137 in this study, where urn:x-wiley:19422466:media:jame20358:jame20358-math-0138 is the field capacity of soil layer urn:x-wiley:19422466:media:jame20358:jame20358-math-0139, urn:x-wiley:19422466:media:jame20358:jame20358-math-0140 is the weight of soil layer urn:x-wiley:19422466:media:jame20358:jame20358-math-0141 during period urn:x-wiley:19422466:media:jame20358:jame20358-math-0142, and urn:x-wiley:19422466:media:jame20358:jame20358-math-0143, where urn:x-wiley:19422466:media:jame20358:jame20358-math-0144 is the total number of soil layers. urn:x-wiley:19422466:media:jame20358:jame20358-math-0145 is determined by the root biomass proportion in the current layer as well as in the wettest layer.

    The urn:x-wiley:19422466:media:jame20358:jame20358-math-0146 for the wettest soil layer is calculated as

    urn:x-wiley:19422466:media:jame20358:jame20358-math-0147(12)
    where superscript urn:x-wiley:19422466:media:jame20358:jame20358-math-0148 denotes the index of the wettest layer; urn:x-wiley:19422466:media:jame20358:jame20358-math-0149 is the proportion of root biomass ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0150) in the wettest soil layer during period urn:x-wiley:19422466:media:jame20358:jame20358-math-0151; urn:x-wiley:19422466:media:jame20358:jame20358-math-0152 is a factor to enlarge the weight of wettest soil layer ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0153), where urn:x-wiley:19422466:media:jame20358:jame20358-math-0154 = 0 indicates that the wettest soil layer is equally weighted with the other layers, and urn:x-wiley:19422466:media:jame20358:jame20358-math-0155 = 1 indicates that the WSF is totally determined by the wettest soil layer. urn:x-wiley:19422466:media:jame20358:jame20358-math-0156 is fixed to 0.5 in this study. The urn:x-wiley:19422466:media:jame20358:jame20358-math-0157 of the remaining layers is calculated as
    urn:x-wiley:19422466:media:jame20358:jame20358-math-0158(13)
    where urn:x-wiley:19422466:media:jame20358:jame20358-math-0159 is the proportion of root biomass ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0160) in soil layer urn:x-wiley:19422466:media:jame20358:jame20358-math-0161 during period urn:x-wiley:19422466:media:jame20358:jame20358-math-0162, and urn:x-wiley:19422466:media:jame20358:jame20358-math-0163.

  2. Proportion of root biomass, urn:x-wiley:19422466:media:jame20358:jame20358-math-0164, in soil layer.

    We assume that the pixel of remote sensing images consists of urn:x-wiley:19422466:media:jame20358:jame20358-math-0165 different components and that urn:x-wiley:19422466:media:jame20358:jame20358-math-0166 includes VRD information of all these components. Therefore, at a pixel scale, we propose that urn:x-wiley:19422466:media:jame20358:jame20358-math-0167 is calculated as

    urn:x-wiley:19422466:media:jame20358:jame20358-math-0168(14)
    where the subscript urn:x-wiley:19422466:media:jame20358:jame20358-math-0169 denotes the index of the surface component; urn:x-wiley:19422466:media:jame20358:jame20358-math-0170 represents the proportion of root biomass of surface components urn:x-wiley:19422466:media:jame20358:jame20358-math-0171 within soil layer urn:x-wiley:19422466:media:jame20358:jame20358-math-0172 during period urn:x-wiley:19422466:media:jame20358:jame20358-math-0173, and urn:x-wiley:19422466:media:jame20358:jame20358-math-0174 is the fractional cover of surface components urn:x-wiley:19422466:media:jame20358:jame20358-math-0175 during period urn:x-wiley:19422466:media:jame20358:jame20358-math-0176.

    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:

    urn:x-wiley:19422466:media:jame20358:jame20358-math-0177(15)
    where urn:x-wiley:19422466:media:jame20358:jame20358-math-0178 is the cumulative root biomass proportion (0–1) of the plant below soil depth urn:x-wiley:19422466:media:jame20358:jame20358-math-0179 (cm) and urn:x-wiley:19422466:media:jame20358:jame20358-math-0180 is the extinction coefficient ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0181), which varies among different biome types. High values of urn:x-wiley:19422466:media:jame20358:jame20358-math-0182 correspond to a greater proportion of root biomass at depth [Jackson et al., 1996, 1997]. Therefore, the root biomass proportion within soil layer urn:x-wiley:19422466:media:jame20358:jame20358-math-0183 of surface component urn:x-wiley:19422466:media:jame20358:jame20358-math-0184, urn:x-wiley:19422466:media:jame20358:jame20358-math-0185, is calculated as
    urn:x-wiley:19422466:media:jame20358:jame20358-math-0186(16)
    where urn:x-wiley:19422466:media:jame20358:jame20358-math-0187 and urn:x-wiley:19422466:media:jame20358:jame20358-math-0188 are the depths of the top boundary and bottom boundary of soil layer urn:x-wiley:19422466:media:jame20358:jame20358-math-0189, respectively, and urn:x-wiley:19422466:media:jame20358:jame20358-math-0190 is the root extinction coefficient of surface component urn:x-wiley:19422466:media:jame20358:jame20358-math-0191. Specially, for the shallowest layer ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0192 = 1), urn:x-wiley:19422466:media:jame20358:jame20358-math-0193 = 0, and for the deepest layer, we set urn:x-wiley:19422466:media:jame20358:jame20358-math-0194= 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0195, urn:x-wiley:19422466:media:jame20358:jame20358-math-0196, 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, urn:x-wiley:19422466:media:jame20358:jame20358-math-0197, is calculated as

    urn:x-wiley:19422466:media:jame20358:jame20358-math-0198(17)
    where urn:x-wiley:19422466:media:jame20358:jame20358-math-0199 is the total fractional cover of vegetation during period urn:x-wiley:19422466:media:jame20358:jame20358-math-0200, 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0201 as
    urn:x-wiley:19422466:media:jame20358:jame20358-math-0202(18)
    where urn:x-wiley:19422466:media:jame20358:jame20358-math-0203 and urn:x-wiley:19422466:media:jame20358:jame20358-math-0204 are the urn:x-wiley:19422466:media:jame20358:jame20358-math-0205 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0206, urn:x-wiley:19422466:media:jame20358:jame20358-math-0207, is
    urn:x-wiley:19422466:media:jame20358:jame20358-math-0208(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]. urn:x-wiley:19422466:media:jame20358:jame20358-math-0209 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0210 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. urn:x-wiley:19422466:media:jame20358:jame20358-math-0211 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0212 value for bare soil is 0; this value indicates that bare soil merely uptakes water from the shallowest soil layer.

Table 2. urn:x-wiley:19422466:media:jame20358:jame20358-math-0213 Values of for Overstory Species, Understory Species, and Bare Soil Biomes of EBF, DBF, ENF, SHR, GRA, SAV, and CRO
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

Temporally continuous soil water content (SWC) information is not globally available; therefore, we derive this here from a multilayer soil water balance module modified from that introduced by Miralles et al. [2011]. The soil water balance module has no more than three soil layers, and the maximum depth of the third soil layer is 250 cm. However, the number of soil layers at a specific site depends on the depth of the entire soil profile ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0214). For different urn:x-wiley:19422466:media:jame20358:jame20358-math-0215 values, the soil layers are specified as
  1. for urn:x-wiley:19422466:media:jame20358:jame20358-math-0216 10 cm: 0–D;
  2. for 10 cm urn:x-wiley:19422466:media:jame20358:jame20358-math-0217 100 cm: 0–10 cm and 10 cm–D;
  3. for urn:x-wiley:19422466:media:jame20358:jame20358-math-0218 > 100 cm: 0–10 cm, 10–100 cm, and 100– urn:x-wiley:19422466:media:jame20358:jame20358-math-0219.
The water loss from each soil layer by evapotranspiration is determined by urn:x-wiley:19422466:media:jame20358:jame20358-math-0220, and rainfall and snowmelt are considered as the input water sources (Figure 1). The soil water budget of the entire soil profile on a daily step is described as
urn:x-wiley:19422466:media:jame20358:jame20358-math-0221(20)
where urn:x-wiley:19422466:media:jame20358:jame20358-math-0222 is the soil water change of the entire soil profile (mm) during period urn:x-wiley:19422466:media:jame20358:jame20358-math-0223 and urn:x-wiley:19422466:media:jame20358:jame20358-math-0224 is the estimated actual evapotranspiration (mm) calculated using equation 5. urn:x-wiley:19422466:media:jame20358:jame20358-math-0225 is assumed to consume first the input water source and then the residual consumes the soil water. Based on this assumption, the water budget of soil layer urn:x-wiley:19422466:media:jame20358:jame20358-math-0226 is modeled as follows:
  1. For urn:x-wiley:19422466:media:jame20358:jame20358-math-0227, the change in soil water of layer urn:x-wiley:19422466:media:jame20358:jame20358-math-0228, urn:x-wiley:19422466:media:jame20358:jame20358-math-0229, depends on urn:x-wiley:19422466:media:jame20358:jame20358-math-0230 and the total loss of water from the entire soil profile, such that

    urn:x-wiley:19422466:media:jame20358:jame20358-math-0231(21)
    where urn:x-wiley:19422466:media:jame20358:jame20358-math-0232 is the soil water content (mm) of layer urn:x-wiley:19422466:media:jame20358:jame20358-math-0233 in the next period.

  2. For urn:x-wiley:19422466:media:jame20358:jame20358-math-0234, urn:x-wiley:19422466:media:jame20358:jame20358-math-0235 is calculated as follows:

    urn:x-wiley:19422466:media:jame20358:jame20358-math-0236(22)
    urn:x-wiley:19422466:media:jame20358:jame20358-math-0237(23)
    where urn:x-wiley:19422466:media:jame20358:jame20358-math-0238 represents the water infiltrated from layer urn:x-wiley:19422466:media:jame20358:jame20358-math-0239 to urn:x-wiley:19422466:media:jame20358:jame20358-math-0240; and water from layer urn:x-wiley:19422466:media:jame20358:jame20358-math-0241 to layer urn:x-wiley:19422466:media:jame20358:jame20358-math-0242, urn:x-wiley:19422466:media:jame20358:jame20358-math-0243, is the residual of urn:x-wiley:19422466:media:jame20358:jame20358-math-0244 after filling soil layer urn:x-wiley:19422466:media:jame20358:jame20358-math-0245 (see equation 23). Specially, for the first layer: urn:x-wiley:19422466:media:jame20358:jame20358-math-0246 =  urn:x-wiley:19422466:media:jame20358:jame20358-math-0247.

2.1.4 Implementing the Model

In this study, the model is implemented on a daily step. For long-term implementation, the urn:x-wiley:19422466:media:jame20358:jame20358-math-0248 of each day can be derived if the soil water content of each soil layer at the first day, urn:x-wiley:19422466:media:jame20358:jame20358-math-0249, is given. We derive urn:x-wiley:19422466:media:jame20358:jame20358-math-0250 using the following steps:
  1. Let urn:x-wiley:19422466:media:jame20358:jame20358-math-0251, and use this initial value to simulate time series urn:x-wiley:19422466:media:jame20358:jame20358-math-0252 values.
  2. Calculate the 16 day urn:x-wiley:19422466:media:jame20358:jame20358-math-0253 of each soil layer in each year: the sequence number of 16 day periods in each year is defined as urn:x-wiley:19422466:media:jame20358:jame20358-math-0254, where urn:x-wiley:19422466:media:jame20358:jame20358-math-0255 is the Julian day.
  3. Interannually average 16 day urn:x-wiley:19422466:media:jame20358:jame20358-math-0256 with the corresponding sequence number (the first 16 day period is excluded).
  4. The urn:x-wiley:19422466:media:jame20358:jame20358-math-0257 value of the first day is assumed to be the interannually averaged urn:x-wiley:19422466:media:jame20358:jame20358-math-0258 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, urn:x-wiley:19422466:media:jame20358:jame20358-math-0259, is used at every site. For sites with data covering only 1 year, the last 16 day urn:x-wiley:19422466:media:jame20358:jame20358-math-0260 of this year is used as urn:x-wiley:19422466:media:jame20358:jame20358-math-0261.

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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0262 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.

Table 3. Descriptions of the Four Older PM-Based Models
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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0263 Leuning et al. [2008] and Zhang et al. [2010]
4 Mu2007 urn:x-wiley:19422466:media:jame20358:jame20358-math-0264 Mu et al. [2007]
  • a urn:x-wiley:19422466:media:jame20358:jame20358-math-0265: water stress factor for soil evaporation, urn:x-wiley:19422466:media:jame20358:jame20358-math-0266: available energy for canopy transpiration, urn:x-wiley:19422466:media:jame20358:jame20358-math-0267: maximum stomatal conductance at the top of the canopy, urn:x-wiley:19422466:media:jame20358:jame20358-math-0268: visible radiation at the top of the canopy, urn:x-wiley:19422466:media:jame20358:jame20358-math-0269: leaf area index of canopy, urn:x-wiley:19422466:media:jame20358:jame20358-math-0270: available energy for soil transpiration, urn:x-wiley:19422466:media:jame20358:jame20358-math-0271: relative humidity of air, urn:x-wiley:19422466:media:jame20358:jame20358-math-0272: mean stomatal conductance coefficient, urn:x-wiley:19422466:media:jame20358:jame20358-math-0273: constraint factor of air temperature to stomatal conductance, urn:x-wiley:19422466:media:jame20358:jame20358-math-0274: constraint factor of urn:x-wiley:19422466:media:jame20358:jame20358-math-0275 to stomatal conductance. For the meaning of other symbols, please see equation 1.
The aerodynamic conductance algorithm of Thom [1975] was applied to the Mu2007, Zh2010, Ye-VI, and RS-WBPM models, and is
urn:x-wiley:19422466:media:jame20358:jame20358-math-0276(24)
where urn:x-wiley:19422466:media:jame20358:jame20358-math-0277 is the von Karman's constant 0.41, urn:x-wiley:19422466:media:jame20358:jame20358-math-0278 is wind speed ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0279) at reference height urn:x-wiley:19422466:media:jame20358:jame20358-math-0280 (m), urn:x-wiley:19422466:media:jame20358:jame20358-math-0281 is zero displacement height (m), urn:x-wiley:19422466:media:jame20358:jame20358-math-0282 is roughness height for momentum transfer (m), and urn:x-wiley:19422466:media:jame20358:jame20358-math-0283 is roughness height for vapor transfer (m). urn:x-wiley:19422466:media:jame20358:jame20358-math-0284, urn:x-wiley:19422466:media:jame20358:jame20358-math-0285, and urn:x-wiley:19422466:media:jame20358:jame20358-math-0286 are estimated using the following equations:
urn:x-wiley:19422466:media:jame20358:jame20358-math-0287(25)
urn:x-wiley:19422466:media:jame20358:jame20358-math-0288(26)
urn:x-wiley:19422466:media:jame20358:jame20358-math-0289(27)
where urn:x-wiley:19422466:media:jame20358:jame20358-math-0290 is the mean canopy height of the evapotranspiration source (m). The stability parameter of the atmosphere is excluded in equation 24 and this simplification may introduce 25% uncertainties to urn:x-wiley:19422466:media:jame20358:jame20358-math-0291 [Leuning et al., 2008]. However, urn:x-wiley:19422466:media:jame20358:jame20358-math-0292 is insensitive to uncertainties of urn:x-wiley:19422466:media:jame20358:jame20358-math-0293 at a daily scale [Leuning et al., 2008; Zhang et al., 2008]. A comparison between the different model scenarios of PM models using different urn:x-wiley:19422466:media:jame20358:jame20358-math-0294 algorithms shows that the algorithm of Thom [1975] performs best for most biome types [Ershadi et al., 2015].

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 ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0295), sensible heat flux ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0296), and net radiation ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0297)) and meteorological variables (e.g., air temperature, relative humidity, saturated vapor pressure deficit, and precipitation).

Details are in the caption following the image

Distribution of the 27 eddy covariance flux towers used in this study.

Table 4. Names of Flux Sites (Site Name), Site Code, Biome Types (Biome), Latitude (Lat), Longitude (Lon), Mean Canopy Height of Dominating Species (HC), Annual Mean Precipitation (P), and Years (Years) for the Flux Sites Used in This Study and Their Citations
 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 ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0298, where urn:x-wiley:19422466:media:jame20358:jame20358-math-0299 and urn:x-wiley:19422466:media:jame20358:jame20358-math-0300 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 ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0301), temperature ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0302), saturated vapor pressure deficit ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0303), and precipitation ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0304) 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0305 by all ET models in this study was compared with site observed urn:x-wiley:19422466:media:jame20358:jame20358-math-0306, 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0308) were retrieved values scaled by urn:x-wiley:19422466:media:jame20358:jame20358-math-0309.

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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0310 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0311 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0312 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0313 parameterized with EVI (Ye-EVI) and NDVI (Ye-NDVI), respectively. When estimating the VI-based urn:x-wiley:19422466:media:jame20358:jame20358-math-0314, equation 4 is incorporated in both Ye-EVI and Ye-NDVI. Figure 3 shows temporal variations of urn:x-wiley:19422466:media:jame20358:jame20358-math-0315 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 ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0316 =  urn:x-wiley:19422466:media:jame20358:jame20358-math-0317, urn:x-wiley:19422466:media:jame20358:jame20358-math-0318 =  urn:x-wiley:19422466:media:jame20358:jame20358-math-0319, urn:x-wiley:19422466:media:jame20358:jame20358-math-0320 and urn:x-wiley:19422466:media:jame20358:jame20358-math-0321 denote averaged urn:x-wiley:19422466:media:jame20358:jame20358-math-0322 and RMSE of all the crop sites, which is the same for other biomes), Ye-NDVI for DBF ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0323 = urn:x-wiley:19422466:media:jame20358:jame20358-math-0324, urn:x-wiley:19422466:media:jame20358:jame20358-math-0325 = urn:x-wiley:19422466:media:jame20358:jame20358-math-0326), Zh2010 for EBF ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0327 =  urn:x-wiley:19422466:media:jame20358:jame20358-math-0328, urn:x-wiley:19422466:media:jame20358:jame20358-math-0329 =  urn:x-wiley:19422466:media:jame20358:jame20358-math-0330), and ENF ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0331 =  urn:x-wiley:19422466:media:jame20358:jame20358-math-0332, urn:x-wiley:19422466:media:jame20358:jame20358-math-0333 = urn:x-wiley:19422466:media:jame20358:jame20358-math-0334), Mu2011 for GRA ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0335 =  urn:x-wiley:19422466:media:jame20358:jame20358-math-0336, urn:x-wiley:19422466:media:jame20358:jame20358-math-0337 =  urn:x-wiley:19422466:media:jame20358:jame20358-math-0338) and Mu2007 for SHR ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0339 =  urn:x-wiley:19422466:media:jame20358:jame20358-math-0340, urn:x-wiley:19422466:media:jame20358:jame20358-math-0341 = urn:x-wiley:19422466:media:jame20358:jame20358-math-0342) and SAV ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0343 =  urn:x-wiley:19422466:media:jame20358:jame20358-math-0344, urn:x-wiley:19422466:media:jame20358:jame20358-math-0345 =  urn:x-wiley:19422466:media:jame20358:jame20358-math-0346).

Details are in the caption following the image

Temporal variation in daily urn:x-wiley:19422466:media:jame20358:jame20358-math-0347 estimated by four PM-based models, and observed flux at 27 flux sites.

Details are in the caption following the image

Coefficient of determination ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0348), root mean standard error (RMSE), and bias (Bias) of observed daily urn:x-wiley:19422466:media:jame20358:jame20358-math-0349 versus estimated urn:x-wiley:19422466:media:jame20358:jame20358-math-0350 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0351 at few sites (Figure 3). For most sites, PMOVs tend to yield unreliable estimation for urn:x-wiley:19422466:media:jame20358:jame20358-math-0352 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0353. 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0354 at most forest sites (e.g., US-Me2, US-Blo, IT-Ro2, and IT-CA3) in summer; Mu2007 and Mu2011 overestimated urn:x-wiley:19422466:media:jame20358:jame20358-math-0355 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0357 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0358 versus estimated urn:x-wiley:19422466:media:jame20358:jame20358-math-0359 by RS-WBPM-EVI, RS-WBPM-NDVI, and OMOV are shown in Figure 5. Figure 6 shows the temporal variation of observed 16 day urn:x-wiley:19422466:media:jame20358:jame20358-math-0360 and estimated 16 day urn:x-wiley:19422466:media:jame20358:jame20358-math-0361 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.

Details are in the caption following the image

Scatterplots of observed daily urn:x-wiley:19422466:media:jame20358:jame20358-math-0362 versus estimated urn:x-wiley:19422466:media:jame20358:jame20358-math-0363 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.

Details are in the caption following the image

Temporal variations in observed 16 day urn:x-wiley:19422466:media:jame20358:jame20358-math-0364 (observed), estimated urn:x-wiley:19422466:media:jame20358:jame20358-math-0365 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.

Details are in the caption following the image

Coefficient of determination ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0366), root mean standard error (RMSE), and bias (Bias) of observed daily urn:x-wiley:19422466:media:jame20358:jame20358-math-0367 versus estimated urn:x-wiley:19422466:media:jame20358:jame20358-math-0368 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0369 ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0370) of 0.59 urn:x-wiley:19422466:media:jame20358:jame20358-math-0371) and 0.55 urn:x-wiley:19422466:media:jame20358:jame20358-math-0372) for all 27 sites, respectively, while OMOV yields urn:x-wiley:19422466:media:jame20358:jame20358-math-0373 ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0374) of 0.50 urn:x-wiley:19422466:media:jame20358:jame20358-math-0375). This result also demonstrates that RS-WBPM-EVI better estimates daily urn:x-wiley:19422466:media:jame20358:jame20358-math-0376 than RS-WBPM-NDVI. However, Figure 7 shows some differences. RS-WBPM-NDVI performs better than RS-WBPM-EVI for SHR with urn:x-wiley:19422466:media:jame20358:jame20358-math-0377 ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0378) of 0.53 ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0379), 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0380 ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0381) of 0.64 (15.15 urn:x-wiley:19422466:media:jame20358:jame20358-math-0382), 0.53 (13.54 urn:x-wiley:19422466:media:jame20358:jame20358-math-0383), and 0.79 (13.39 urn:x-wiley:19422466:media:jame20358:jame20358-math-0384) on a daily scale for GRA, SHR, and SAV, respectively, which is 0.20 (1.96 urn:x-wiley:19422466:media:jame20358:jame20358-math-0385), 0.19 (1.57 urn:x-wiley:19422466:media:jame20358:jame20358-math-0386), and 0.19 (5.75 urn:x-wiley:19422466:media:jame20358:jame20358-math-0387) higher (lower) than that of OMOV. With the recommended VI, RS-WBPM yields urn:x-wiley:19422466:media:jame20358:jame20358-math-0388 ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0389) of 0.44 (34.94 urn:x-wiley:19422466:media:jame20358:jame20358-math-0390), 0.78 (21.97 urn:x-wiley:19422466:media:jame20358:jame20358-math-0391), 0.57 (16.65 urn:x-wiley:19422466:media:jame20358:jame20358-math-0392), and 0.60 (18.54 urn:x-wiley:19422466:media:jame20358:jame20358-math-0393) for daily urn:x-wiley:19422466:media:jame20358:jame20358-math-0394 of CRO, DBF, EBF, and ENF, respectively. In addition, at all 27 sites, it yields urn:x-wiley:19422466:media:jame20358:jame20358-math-0395 ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0396) of 0.60 urn:x-wiley:19422466:media:jame20358:jame20358-math-0397) for daily urn:x-wiley:19422466:media:jame20358:jame20358-math-0398 (Figure 8a).

Details are in the caption following the image

Scatterplots of observed daily urn:x-wiley:19422466:media:jame20358:jame20358-math-0399 versus estimated urn:x-wiley:19422466:media:jame20358:jame20358-math-0400 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0401 ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0402) of 0.62 urn:x-wiley:19422466:media:jame20358:jame20358-math-0403) 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0404 are better captured by RS-WBPM than OMOV at nonagricultural sites. OMOV significantly overestimates urn:x-wiley:19422466:media:jame20358:jame20358-math-0405 at ES-ES1, FR-Pue, IT-Noe, US-Ton, and US-Var in the dry season, but underestimates urn:x-wiley:19422466:media:jame20358:jame20358-math-0406 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0407 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.

Table 5. Comparison of Coefficients of Determination of RS-WBPM Parameterized by ES-EVI With PT-JPL Model and Other Models Incorporating a Soil Water Balance Modela
Site Model urn:x-wiley:19422466:media:jame20358:jame20358-math-0408 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- urn:x-wiley:19422466:media:jame20358:jame20358-math-0409) 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- urn:x-wiley:19422466:media:jame20358:jame20358-math-0410) 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- urn:x-wiley:19422466:media:jame20358:jame20358-math-0411) 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- urn:x-wiley:19422466:media:jame20358:jame20358-math-0412) 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0413 at US-Ton, PT-Mi2, and IT-Noe sites, but lower urn:x-wiley:19422466:media:jame20358:jame20358-math-0414 than GLEAM at ES-LMa site. On a monthly scale, RS-WBPM also yields higher urn:x-wiley:19422466:media:jame20358:jame20358-math-0415 at US-Ton and PT-Mi2 sites, and comparable urn:x-wiley:19422466:media:jame20358:jame20358-math-0416 at ES-LMa site. Compared with the urn:x-wiley:19422466:media:jame20358:jame20358-math-0417 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0418 were primarily caused by uncertainties in input precipitation. After substituting the ERA-Interim precipitation for the in situ value, RS-WBPM yielded urn:x-wiley:19422466:media:jame20358:jame20358-math-0419 of 0.53 for daily urn:x-wiley:19422466:media:jame20358:jame20358-math-0420 and 0.92 for monthly urn:x-wiley:19422466:media:jame20358:jame20358-math-0421 at ES-LMa. Simulation of RS-WBPM in arid and semiarid regions highly depends on the input water source. Descending values of urn:x-wiley:19422466:media:jame20358:jame20358-math-0422 for daily urn:x-wiley:19422466:media:jame20358:jame20358-math-0423 at ES-LMa demonstrates that uncertainties of input precipitation will significantly affect RS-WBPM's estimation of daily soil water content, and therefore daily urn:x-wiley:19422466:media:jame20358:jame20358-math-0424. 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0425 to that of the ARTS E model [Yan et al., 2012] at US-Ton and US-Me2 sites, but significantly higher urn:x-wiley:19422466:media:jame20358:jame20358-math-0426 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, urn:x-wiley:19422466:media:jame20358:jame20358-math-0427, and soil moisture is derived from a water balance model. This method performs well with site-based optimum, urn:x-wiley:19422466:media:jame20358:jame20358-math-0428, but when the model is parameterized by plant-functional-type-based coefficients (PFT- urn:x-wiley:19422466:media:jame20358:jame20358-math-0429), urn:x-wiley:19422466:media:jame20358:jame20358-math-0430 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0431 is not shown in Table 5). RS-WBPM-EVI shows a comparable result to CONUS-PT with site-based optimum urn:x-wiley:19422466:media:jame20358:jame20358-math-0432, 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0433 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0434 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0435 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0436

Although VIs are useful in parameterizing urn:x-wiley:19422466:media:jame20358:jame20358-math-0437 [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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0438 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, urn:x-wiley:19422466:media:jame20358:jame20358-math-0439 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0440 of EBF, GRA, SHR, and SAV was significantly overestimated by the Ye-VI algorithm in the dry season.

Another limitation of the cross-calibrated urn:x-wiley:19422466:media:jame20358:jame20358-math-0441 algorithm is that it does not estimate the differences between magnitudes of urn:x-wiley:19422466:media:jame20358:jame20358-math-0442 in differing biomes. The urn:x-wiley:19422466:media:jame20358:jame20358-math-0443 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0444 value at a pixel scale, it may be inappropriate on a global scale. The parameterization of urn:x-wiley:19422466:media:jame20358:jame20358-math-0445 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0446. Therefore, a simple correction factor, urn:x-wiley:19422466:media:jame20358:jame20358-math-0447 (see equation 4), is used to scale the result of equation 3. As the urn:x-wiley:19422466:media:jame20358:jame20358-math-0448 of EBF in the AMC was significantly overestimated by equation 3. The estimations of urn:x-wiley:19422466:media:jame20358:jame20358-math-0449 by Ye-EVI with urn:x-wiley:19422466:media:jame20358:jame20358-math-0450 and urn:x-wiley:19422466:media:jame20358:jame20358-math-0451 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0452 means that the value of urn:x-wiley:19422466:media:jame20358:jame20358-math-0453 is calculated using equation 3 without correction with urn:x-wiley:19422466:media:jame20358:jame20358-math-0454. 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0455 and urn:x-wiley:19422466:media:jame20358:jame20358-math-0456 yields the same urn:x-wiley:19422466:media:jame20358:jame20358-math-0457; however, Ye-EVI with urn:x-wiley:19422466:media:jame20358:jame20358-math-0458 yields lower RMSE, while the Ye-EVI with urn:x-wiley:19422466:media:jame20358:jame20358-math-0459 significantly overestimates urn:x-wiley:19422466:media:jame20358:jame20358-math-0460. This implies the necessity of correcting to urn:x-wiley:19422466:media:jame20358:jame20358-math-0461. However, using urn:x-wiley:19422466:media:jame20358:jame20358-math-0462 to scale urn:x-wiley:19422466:media:jame20358:jame20358-math-0463 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0464 using VI based on the plant functional type (PFT), as it is anticipated that this would help improve the RS-WBPM model.

Details are in the caption following the image

Scatterplots of observed daily urn:x-wiley:19422466:media:jame20358:jame20358-math-0465 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) urn:x-wiley:19422466:media:jame20358:jame20358-math-0466 = 1 and (b) urn:x-wiley:19422466:media:jame20358:jame20358-math-0467 = 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).

Table 6. Correlation Coefficient (R1 and R2) Between Daily Soil Water Content Simulated by RS-WBPM-EVI/RS-WBPM-NDVI and That Observed at 23 Flux Sitesa
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 ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0468) of the soil, which is the difference between wilting point ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0469) and field capacity ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0470). As errors of urn:x-wiley:19422466:media:jame20358:jame20358-math-0471 or urn:x-wiley:19422466:media:jame20358:jame20358-math-0472 will introduce errors to urn:x-wiley:19422466:media:jame20358:jame20358-math-0473, 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0474 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0475.

We therefore reran the RS-WBPM model using in situ meteorological data and urn:x-wiley:19422466:media:jame20358:jame20358-math-0476 with perturbations; anomalies of urn:x-wiley:19422466:media:jame20358:jame20358-math-0477 and RMSE of RS-WBPM-EVI model incorporating urn:x-wiley:19422466:media:jame20358:jame20358-math-0478 with perturbations are presented (Figure 10) and perturbations of urn:x-wiley:19422466:media:jame20358:jame20358-math-0479 are specified as [−25, 25%], with a variation step of 5%.

Details are in the caption following the image

Response of (a) urn:x-wiley:19422466:media:jame20358:jame20358-math-0480 and (b) RMSE of RS-WBPM-EVI simulating urn:x-wiley:19422466:media:jame20358:jame20358-math-0481 to errors of soil water holding capacity ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0482) 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0483, as shown by the lines of mean anomalies of urn:x-wiley:19422466:media:jame20358:jame20358-math-0484 (Figure 10a) and RMSE (Figure 10b), which do not fluctuate significantly with variation in urn:x-wiley:19422466:media:jame20358:jame20358-math-0485 errors. The results also show that the anomalies of urn:x-wiley:19422466:media:jame20358:jame20358-math-0486 and RMSE strengthen with an increase in the absolute values of the relative errors. urn:x-wiley:19422466:media:jame20358:jame20358-math-0487 (RMSE) of RS-WBPM incorporating urn:x-wiley:19422466:media:jame20358:jame20358-math-0488 with perturbations of −25% has the strongest anomalies, −0.094 to 0.022 (−3.34 to 4.31 urn:x-wiley:19422466:media:jame20358:jame20358-math-0489). However, the anomalies of urn:x-wiley:19422466:media:jame20358:jame20358-math-0490 (RMSE) of RS-WBPM with urn:x-wiley:19422466:media:jame20358:jame20358-math-0491 with urn:x-wiley:19422466:media:jame20358:jame20358-math-0492 perturbations fluctuate between −0.048 and 0.028 (−0.92 and urn:x-wiley:19422466:media:jame20358:jame20358-math-0493), and the anomaly intensity of urn:x-wiley:19422466:media:jame20358:jame20358-math-0494 (RMSE) decreases with the error. This analysis indicates that if the relative error of urn:x-wiley:19422466:media:jame20358:jame20358-math-0495 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0496 for most biome types. The improvement in the RS-WBPM model was most apparent when simulating the urn:x-wiley:19422466:media:jame20358:jame20358-math-0497 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0498 (RMSE = 18.72 urn:x-wiley:19422466:media:jame20358:jame20358-math-0499) 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0500 was also addressed in this study, and it is considered that a biome-based correction factor urn:x-wiley:19422466:media:jame20358:jame20358-math-0501 could help the RS-WBPM more accurately simulate urn:x-wiley:19422466:media:jame20358:jame20358-math-0502; 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 ( urn:x-wiley:19422466:media:jame20358:jame20358-math-0503), but it was found that errors of urn:x-wiley:19422466:media:jame20358:jame20358-math-0504 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 urn:x-wiley:19422466:media:jame20358:jame20358-math-0505 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.