A time domain triangle method approach to estimate ...

Remote Sensing of Environment 174 (2016) 10–23

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A time domain triangle method approach to estimate actual evapotranspiration: Application in a Mediterranean region using MODIS and MSG-SEVIRI products Mario Minacapilli a, Simona Consoli b,⁎, Daniela Vanella b, Giuseppe Ciraolo c, Antonio Motisi a a b c

University of Palermo, Dipartimento di Scienze Agrarie e Forestali (SAF), V.le delle Scienze Ed. 4., 90128, Palermo, Italy University of Catania, Dipartimento di Agricoltura, Alimentazione e Ambiente (Di3A), Via S. Sofia, 100, 95123 Catania, Italy University of Palermo, Department of Civil, Environmental, Aerospace, Materials Engineering (DICAM), V.le delle Scienze Ed. 8, 90128 Palermo, Italy

a r t i c l e

i n f o

Article history: Received 15 May 2015 Received in revised form 10 December 2015 Accepted 11 December 2015 Available online xxxx Keywords: Evapotranspiration Time series LST EVI MODIS MSG-SEVIRI Eddy covariance

a b s t r a c t In this study, spatially distributed estimates of regional actual evapotranspiration (ET) were obtained using a revised procedure of the so called “triangle method” to parameterize the Priestley–Taylor ϕ coefficient. In the procedure herein proposed, named Time-Domain Triangle Method (TDTM), the triangular feature space was parameterized considering pairs of Ts–VI values obtained by exploring, for each pixel, only their temporal dynamics. This new method was developed using time series products provided by MODIS and MSG-SEVIRI sensors. Moreover the proposed procedure does not depend on ancillary data, and it is only based on remotely sensed vegetation indices and day–night time land surface temperature differences. Two different test areas located in Sicily were selected for testing and validating the approach. Satellite ET rates were validated versus directly measured fluxes of mass (ET) obtained by eddy covariance (EC) towers during the observation period 2010–2012. The proposed approach predicts daily ET rates with an acceptable level of accuracy for practical purposes; therefore, the TDTM can be considered as a simple and effective tool to easily estimate, at regional scale, spatial and temporal changes of this key-variable related to water resource management, agriculture, ecology and climate change. © 2015 Published by Elsevier Inc.

1. Introduction Evapotranspiration (ET) is a key variable that plays a strategic role in the fields of water resource management, agriculture, ecology and climate change (Sobrino, Gómez, Jiménez-Muñoz, & Olioso, 2007; Chirouze et al., 2014). For most of the Mediterranean regions (southern part of Europe), which are usually characterized by semiarid climates and chronic water scarcity, agriculture is the major user of water resources, and hence has significant impacts on water quantity. In these regions, the availability of water is a major limitation on crop production due to insufficient rainfall to compensate the evaporative losses by crops (i.e. more than 80% of the annual available water is lost through evapotranspiration) (Chehbouni et al., 2008). There is therefore a need to rationalize the use of irrigation via monitoring ET process. In particular, continuous and accurate estimation of spatial and temporal ET variations at regional scale is of paramount importance for improving water resources management, drought detection, climate change simulation and mitigation (Wang & Liang, 2008). Although ET at the local

⁎ Corresponding author. E-mail address: [email protected] (S. Consoli).

http://dx.doi.org/10.1016/j.rse.2015.12.018 0034-4257/© 2015 Published by Elsevier Inc.

scale can be accurately estimated from detailed ground-based observations (i.e. eddy covariance, EC; Bowen ratio, BR, etc.), it is much more critical for regional authorities to monitor water allocation and use at the irrigation district or watershed scales. At the regional scale, sufficient ground-point observations, necessary to explore the spatial variability of ET, are often not available; moreover, despite the spatial variability of the footprint area of EC technique (e.g. one of the most used methods for measuring latent heat flux density), its measurement might be considered as an average over the footprint and quite variable in time (Wang & Jia, 2013). Therefore, current field-based measurements cannot capture hydrological processes with adequate reliability over large areas. Spatially distributed remote sensing data can permit reliable descriptions of the observed surface at most scales, ranging from plot to region, and across wide temporal scales depending on the overpass time of remote sensing platforms (Chirouze et al., 2014). The use of remote sensing to estimate ET is presently being developed to retrieve large-scale distribution of land surface parameters such as temperature, albedo, and vegetation indices (Li et al., 2009; Minacapilli et al., 2009; Consoli & Vanella, 2014a), which are essential inputs to remotely sensed ET models application at the regional scale (Tang, Li, & Tang, 2010).

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The use of remote sensing to estimate ET is presently being developed along two approaches: (i) land surface energy balance (EB) methods, which include applications of the Penman–Monteith (P–M) equation, using visible and near infrared spectral bands and ancillary meteorological data (Idso, Schmuggr, Jackson, & Reginato, 1975; Moran, 1989; Norman, Kustas, & Humes, 1995; Chavez, Neale, Hipps, Prueger, & Kustas, 2005; Allen, Tasumi, & Trezza, 2007; González-Dugo et al., 2009; Consoli & Vanella, 2014a); (ii) a reflectance-based vegetation index (VI) approach that relies on the ability of vegetation indices (VIs), derived from surface reflectance data to trace the crop growth and estimate the basal crop coefficient (Kcb) (Minacapilli, Iovino, & D'Urso, 2008;,Glenn, Nagler, & Huete, 2010). This second method determines spatially distributed values of Kcb that capture field-specific crop development and are used to adjust daily reference ET (ET0) estimated from local weather station data (González-Dugo et al., 2013; Consoli & Vanella, 2014b). The main advantage of the VI-based methods is that satellite images in the reflective bands of the spectrum are more readily available than the thermal band data, and generally at higher spatial resolution. However, unless coupled to a soil water balance, this method cannot account for evapotranspiration rate changes due to water stress conditions. In contrast, surface temperature-based methods can readily capture stress effects without requiring ancillary rainfall data and soil hydraulic and texture properties (Anderson, Norman, Mecikalski, Otkin, & Kustas, 2007; González-Dugo et al., 2009; Consoli & Vanella, 2014b). Remotely sensed ET models based on the classic “residual solution” of the surface energy balance, SEB, can be applied using two main schematizations, i.e., “single source” (Bastiaanssen, Menenti, Feddes, & Holtslang, 1998) or “dual source“(Norman et al., 1995). Numerous authors have provided detailed descriptions of these models since 1990s (Kustas & Norman, 1996; Glenn, Huete, Nagler, Hirschboeck, & Brown, 2007; Kalma, McVicar, & McCabe, 2008; Li et al., 2009; Kustas & Anderson, 2009; Minacapilli et al., 2009; Consoli & Vanella, 2014a). For example, well known SEB models, such as SEBAL (surface energy balance algorithm for land, Bastiaanssen et al., 1998) and METRIC (mapping evapotranspiration at high resolution with internalized calibration, Allen et al., 2007), join the use of remote sensing information with ancillary data to derive sensible heat flux (H), net radiation, (Rn), soil heat flux, (G) and instantaneous evapotranspiration, the latter as the residual term of the energy balance equation (Bastiaanssen et al., 1998; Boegh, Soegaard, & Thomsen, 2002; Kustas, Perry, Doraiswamy, & Moran, 1994; Norman et al., 2003). These methods estimate surface resistance adopting various schemes and using radiometric surface temperature and ground ancillary weather data. Other remotely based methodologies require the direct application of the Penman–Monteith equation to estimate regional evapotranspiration (Monteith, 1965). In particular, Mu, Heinsch, Zhao, and Running (2007) proposed a complex model to estimate the crop resistance parameter as a function of Leaf Area Index (LAI) and consequently the monthly crop evapotranspiration using standard MODIS data products coupled with the GMAO climatic database (Ramoelo et al., 2014; Kim, Hwang, Mu, Lee, & Choi, 2012). This approach (Mu et al., 2007; Mu, Zhao, & Running, 2011) was validated using the Ameriflux eddy covariance tower network and adopted by NASA which is presently available as the “MOD16A2-ET” product. However, Ramoelo et al. (2014) expressed concerns on the reliability of “MOD16A2-ET” product to derive crop evapotranspiration data. Questionable product performance can be attributed to both the spatial variability of the retrieval algorithm input data and the coarseness of GMAO climatic database. The described methods have in common the need of ground-based measurements and ancillary data, (i.e. wind speed, air temperature, solar radiation, vegetation height), thus limiting their operational applications to mapping ET at the regional scale. Dependence on ancillary data can be addressed using simplified models based on the interpretation of the so-called “triangle method” obtained from Ts–VIs scatterplots (Carlson, Gillies, & Perry, 1994;

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Carlson, Gillies, & Schmugge, 1995; Jiang & Islam, 1999, 2001; Stisen, Sandholt, Nørgaard, Fensholt, & Jensen, 2008). The method relies on the triangular shape formed by the scatterplots of surface temperature versus vegetation index (VI, such as: normalized difference vegetation index, NDVI, enhanced vegetation index, EVI, fractional cover, Fc), under a wide range of vegetation cover and soil moisture availability, to estimate the evaporative fraction (EF) and ET at the satellite pixel resolution scale. EVI is an optimized index designed to enhance the vegetation signal with improved sensitivity in high biomass regions and to improve the vegetation monitoring. Several triangle method applications have been successfully applied for ET estimation by combining MODIS and AVHRR data (Venturini, Bisht, Islam, & Jiang, 2004; Batra, Islam, Venturini, Bisht, & Jiang, 2006). The reliability of the triangle method depends mainly on the parameterization of the dry and wet edges in the Ts–VI feature space. Jiang and Islam (2001, 2003) have identified the wet edge by using the lowest observed clear pixel surface or air temperature in the image scene; whereas the dry edge has been generally defined by a linear interpolation of pixels with minimum VI and maximum surface temperatures (Stisen et al., 2008). Apart from the specific algorithms used, all the proposed methods adopted for dry and wet edge determination share a “triangular feature space”, obtained by plotting Ts–VI values only collected in a given spatial domain, i.e. two single scene images (Ts and VI) captured in the same time. The use of a spatial domain to obtain the “triangle feature space” involves, as main hypothesis, the assumption of uniform atmospheric conditions over the whole image. To meet this hypothesis, the required extension of the explored surface area, used to collect the Ts–VIs, may be too wide. This assumption is limiting especially when the method is applied at a coarse resolution, such as in regional scale applications, contrasting the need of a large number of pixels to clearly define the key features of the “triangle geometry” (i.e. warm and cold edges). Moreover, the use of only the spatial domain to parameterize the Ts–VI relationship does not take into account the natural crops behaviour (e.g., crop types and phenological variability) related to the atmospheric water demand (e.g., seasonal meteorological variations), and makes the hypothesis of a unique interpretation of the Ts–VIs space unrealistic. In this view, Carlson (2007) proposed the idea of the “universal triangle”, with a further time dimension. This study, starting from an existing spatial-domain solution of the “triangle method” introduced by Jiang and Islam (2001) and then by Stisen et al. (2008), aims at developing a new procedure for identifying reliable boundary conditions of the triangle method. The proposed procedure is based on a pixel by pixel Ts–VI feature space, obtained by exploring the temporal domains over each single image pixel. A single Ts–VI triangle feature space is obtained for each pixel of the image; the triangle contains the whole climatic variability of the Ts–VIs. time series, thus contributing to eliminate the hypothesis of atmospheric homogeneity. Specifically, through this new method, called Time-Domain Triangle Method (TDTM) the following main objectives were pursued: a) to exploit time series products (Ts, VIs, and albedo) provided by MODIS satellite sensors to derive the Ts–VI feature space, based on the temporal dynamic of the observed Ts–VIs pairs; b) to set-up a new parameterization of dry and wet edges over the previously derived Ts–VI feature space; c) to estimate actual regional evapotranspiration by combining the new triangle method approach with MODIS and MSG-SEVIRI products, without using ancillary ground-based data.

The developed procedure for ET estimation was validated through evapotranspiration measurements, carried out using eddy covariance (EC) techniques, in two different test areas in Sicily, during 2010– 2012 period. Once the procedure was validated, it was applied over the entire Sicilian region (insular Italy) for mapping ET rates time series.

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2. Theoretical background and proposed methodology 2.1. Estimation of evapotranspiration by combining Priestley–Taylor equation and the TDTM The TDTM theoretical base for ET estimation is quite similar to that proposed by Stisen et al. (2008), whose equations were substantially replied, but in a different data domain (i.e. time). In the TDTM, the Ts–VI feature space, leaving out the reference at the spatial or temporal domain, allowed to model the ϕ parameter of the Priestley–Taylor formulation, P–T, (Monteith, 1965), used to estimate regional evapotranspiration, (ET). The mathematical expression of P–T equation is:  ET ¼ ϕ  ðRn −GÞ 

 Δ Δþγ

ð1Þ

where, the Priestley–Taylor parameter ϕ represents the actual surface resistance to evapotranspiration; Rn is surface net radiation (W m−2), G is the soil heat flux (W m−2), Δ is the slope of the saturated vapour pressure versus air temperature (kPa K−1), γ is the psychrometric constant (kPa K−1). The parameter ϕ in Eq. (1) seems the same as αPT in the original version of the Priestley–Taylor equation, but a difference in the physical meaning of these two parameters there exists. In fact, αPT is generally interpreted as the ratio of actual evaporation to the equilibrium evaporation (well-watered conditions in case of soil-crop surfaces), and it generally converges to 1.26 (Crago & Brutsaert, 1992). In other terms, the Priestley–Taylor's equation is generally applicable for wet surfaces, whereas Eq. (1) holds for a wide range of surface evaporative conditions, with ϕ varying from 0 to (Δ + γ)/Δ (Tang et al., 2010). The ϕ parameter is also related to the so-called evaporative fraction (Λ), defined as the ratio of evapotranspiration (ET) to available energy (Rn − G): Λ¼

ET Rn −G

ð2Þ

in fact, by combining Eqs. (1) and (2), it is possible to relate Λ and ϕ as in the follows:  Λ ¼ϕ

 Δ Δþγ

ð3Þ

where, Δ (kPa K−1) can be calculated as reported by Allen, Pereira, Raes, and Smith (1998), the psychrometric constant γ (kPa K−1) can be computed using the atmospheric pressure (P, kPa) which depends on the elevation, z (m), of the region of interest (i.e. inferred by the digital elevation model — DEM).

The way to retrieve Rn, G, Δ and γ is reported in the next paragraph, while the ϕ parameter is derived using an interpolation scheme from the two boundary conditions of the Ts–VI feature space (warm and cold edge of Fig. 1). In their studies, Wang, Li, and Cribb (2006) and Stisen et al. (2008), have used the temperature difference ΔTs derived from MSG-SEVIRI (Meteosat Second Generation–Spinning Enhanced Visible and Infrared Imager) plotted against VI (i.e. NDVI) to establish the triangular feature space. Price, 1990 and William, John, & Martha, 2003, indicated that the ΔTs-NDVI space is a triangular shape by analysing data from various remote sensors. These authors have obtained accurate ET estimations by using ΔTs instead of the midday surface temperature (Ts). This increase of accuracy might depend on the thermal inertia concept, included in ΔTs, in which the daily temperature amplitude, as measured by a combination of day and night satellite images, was used to explain the resistance of the surface to external temperature variations. Moreover, in Stisen et al. (2008), the minimum ϕ along the dry edge (see Fig. 1) was non-linearly interpolated with VI values between global minima and maxima, whereas ϕ values for intermediate pixel (ϕi) was linearly interpolated between minimum and maximum ϕ, within each selected VI interval. This means that within each vegetation class, the observed surface temperature ranges from a minimum (ΔTs min, ϕmax), to a maximum (ΔTs max, ϕi,min) with the lowest evaporative cooling (Stisen et al., 2008). This implies that ϕi,min is assigned to a pixel with minimum VI and maximum temperature, whereas a fixed value was used for ϕmax. In line with the above hypothesis, the final expressions proposed by Stisen et al. (2008) are the following:  ϕi; min ¼ ϕ max 

ϕi ¼

a


ΔTsi; max −ΔTsi  ϕ max −ϕi; min þ ϕi; min ΔTsi; max −ΔTsi; min

ð4Þ

ð5Þ

where, ΔTs,i (K) is the land surface temperature difference. The exponent “a”, of Eq. 4 describes not only the kind of interpolation of ϕi, min with respect to NDVI, but also the type of decomposition of the generic line defined by the points (NDVIi, Ti,min) and (NDVIi, Ti,max) (see Fig. 1). In their study, Stisen et al. (2008) suggested the use of a non-linear decomposition setting “a” equals to 2. The argument for applying the nonlinear decomposition follows the non-linear intersection of the observed dry edge and iso-lines of equal moisture availability (Stisen et al., 2008). Starting from Stisen et al. (2008) and related researches (Wang et al., 2006; Tang et al., 2010; Kim & Hogue, 2013), in our study we adopted a non-linear decomposition, but we followed a different criteria for determining “a” and the type of VI. In fact, Eq. 4, implicitly includes the fractional cover, Fc, which is usually computed using remotely sensed variables by the following expression:  Fc ¼

Fig. 1. Simplified Ts–VI feature space. Synthesized from Lambin and Ehrlich (1996); Yang, Wu, Shi, and Yan (2008).

NDVIi −NDVIi; min NDVIi; max −NDVIi; min

VI−VI min VI max −VI min

b :

ð6Þ

In our study, the Eq. 4 was, thus, expressed in term of Fc, through the enhanced vegetation index (EVI), in place of NDVI, since EVI is optimized to improve the vegetation signal and reduce soil background influence (Huete et al., 2002; Yang et al., 2008; Kim & Hogue, 2013). Finally, as previously discussed, in our application the parameterization of the two boundary conditions of triangle method has been developed for each single pixel by exploring the temporal variability of Ts–VIs obtained by MODIS product time series. While in the “classic triangle approach” the data domain is limited to the spatial dimension for a single time instant, in the TDTM approach the data domain is the “time”, and the spatial domain is limited to a single pixel, that is explored using standard time series products.

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Table 1 Relevant spatial and temporal information on MODIS and SEVIRI products used in this studya. Sensor

Platform

Layer

Product name

Pixel size (km)

Temporal resolution (day)

MODIS

Terra Terra + aqua

8 (diurnal–nighttime) 16

MSG

MOD11A2 MOD13A1 MCD43A3 DIDSSF LSA-09 DIDSLF LSA-12

1 0.5

SEVIRI

Ts, ε0 EVI Albedo, α RSS RSL

4

1

a 8-Day data are composed from the daily 1-kilometer land surface temperature product (MOD11A1) and stored on a 1-kilometer sinusoidal grid as the average values of clear-sky temperatures during an 8-day period. Albedo and EVI products are obtained by the 16-day MODIS composite technique selecting, for each pixel, the best observation that occurred in the 16-day reference period. An 8-day phasing in the production of the 16-day composites between Terra and Aqua allows the generation of a combined 8-day time series of VI data.

Therefore, the final equations proposed in this work are the following: ϕi; j; min ¼ ϕ max  Fc ϕi; j ¼

ð7Þ

  ΔTsi; j; max −ΔTsi; j  ϕ max −ϕi; j; min þ ϕi; j; min ΔTsi: j; max −ΔTsi; j; min 

Fc; i; j ¼

EVIi; j −EVIi; j; min EVIi; j; max −EVIi; j; min

ð8Þ

b ð9Þ

where, the subscripts i,j refer to the generic pixel (i,j), whereas the differences (Δ), among minima (min) and maxima (max) variables, have been obtained by analysing the corresponding temporal variability over each pixel, during the whole analysed time period 2010–2012. Specifically, the terms ΔTs,ij (K) were obtained by MODIS products (i.e. 8-day time series of diurnal–night-time land surface temperature differences), as well as EVI (i.e. 8-day time series). The 8-day average Ts time series products were chosen, instead of instantaneous daily land surface temperature values, because of their ease of processing and lower time consumption with respect to daily data. In any case, the proposed methodology may be applied even starting from daily data, after the necessary filtering and/or masking corrections for cloudy zones. Moreover, it can be inferred, that the temporal 8-day step is commonly used for ET estimation at the regional scale (see Kim & Hogue, 2013) and for existing products (MOD16A2). The upper bound of ϕ (ϕmax) is assigned as a constant value (i.e. 1.35 for semi-arid conditions, Pereira, 2004) for all values of EVI, since the maximum evapotranspiration rate is assumed to occur for wet

conditions regardless of vegetation; the exponent “b” of Eq. 9 was set equal to 0.46 to match the satellite-based fractional vegetation cover (Fc) to that typically observed for a wide variety of crops. Minimum and maximum EVI values of Eq. 9 are referred to the whole study period (2010–2012). 2.1.1. Net radiation and soil heat flux estimation In the study, the estimation of the available energy (Rn − G) is based on a satellite stand-alone approach (MODIS-Terra and MSG-SEVIRI). In particular, surface net radiation, Rn (W m−2) is defined as: Rn ¼ RSS↓ −α  RSS↓ þ RSL↓ −RSL↑ −ð1−ε0 Þ  RSL↓

ð10Þ

where, RSS↓ is the incoming shortwave radiation (W m−2), α is the surface albedo, RSL↓ is the downward longwave radiation (W m−2), RSL↑ is the upward longwave radiation (W m−2), and εo is the surface thermal emissivity. The Stefan–Boltzmann equation is used to express the upward longwave radiation: RSL↑ ¼ ε0  σ  T4s;avg

ð11Þ

where, σ is the Stefan–Boltzmann constant (5.67 × 10−8 W m−2 K4), and Ts,avg. (K) is the diurnal–night-time mean surface temperature. The downward longwave radiation, RSL↓, can be estimated as a bulk parameterization, where the radiative flux reaching the surface is

Fig. 2. Example of 8-day average of MODIS and MSG-SEVIRI products utilized in the study; maps are referred to July 2010.

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Fig. 3. Flow-chart of the proposed methodology, including algorithms and remote sensing data.

emitted by an atmospheric layer with emissivity εallsky, and temperature Tsky. RSL↓ ¼ εallsky  σ  T4sky

ð12Þ

Thus, both εallsky e and Tsky are usually estimated as a function of near surface atmospheric temperature and/or water vapour content. Most of the developed bulk parameterizations are valid under clear sky condition only (Swinbank, 1963; Idso & Jackson, 1969; Brutsaert, 1975;

Bastiaanssen et al., 1998; Prata, 1996). All-sky bulk condition parameterizations introduce correction factors; in particular, a function for cloudiness and several formulations were proposed to estimate cloud cover from the fraction between observed solar irradiance and that observed under clear skies (Crawford & Duchon, 1999; Bilbao & de Miguel, 2007). In our study that will be described in the next paragraph, we used the downward solar radiation products provided by EUMETSAT Satellite Application Facility and Land Surface Analysis service (LSA-SAF; http://

Fig. 4. Study area: Sicily (Italy) a) and its primary landuse b); test site 1 (olive) and 2 (citrus) a, b); EC1 and EC2 denote the location of eddy covariance flux towers in the two sites, respectively.

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in VIS-NIR regions, have been carried out to assess empirical equations for G/Rn estimation (Clothier et al., 1986; Choudhury, Idso, & Reginato, 1987; Kustas & Daughtry, 1990; Kustas, Daughtry, & Van Oevelen, 1993; Bastiaanssen, 1995; Murray & Verhoef, 2007). In our case, the following empirical relationship (Kustas & Daughtry, 1990) was adopted: G ¼ ½Γ c ðΓ s −Γ c Þð1−Fc Þ Rn

ð15Þ

where Γs and Γc are, respectively, the ratios between surface heat flux, G, and total net radiation, Rn [W m−2] for bare soil and fully covered surface conditions, and Fc is the vegetation cover fraction. On the basis of observed measurements, in our study, values of Γs = 0.1 and Γc = 0.05 were adopted. 2.2. Remote sensing data Fig. 5. Closure of hourly measured fluxes at the two test sites.

landsaf.meteo.pt/) which generates, at full spatial resolution (3 km pixel size at nadir), maps of downward short- and long-wave solar radiation for Europe, Northern and Southern Africa and South America. All data were also obtained using ancillary weather data provided by the European Centre for Medium-range Weather Forecast (ECMWF).Only their final thematic maps can be downloaded, without the possibility to know the original set of weather data used and/or included. This circumstance did not allow us to know the values of εallsky inside the LSA-SAF product therefore, in our study the following parameterization (Crawford & Duchon, 1999) was adopted: εallsky ¼ εc  ð1−cÞ þ c

ð13Þ

where, εc is the atmospheric emissivity in clear-sky condition (Bastiaanssen et al., 1998) and, c is the cloudiness factor determined as in the follows: c ¼ 1−

RSS↓ Ra

ð14Þ

where RSS↓ the incoming shortwave radiation provided by LSA-SAF and Ra (W m−2), is the theoretical clear sky downward solar radiation (Allen et al., 1998). Soil heat flux (G, W m−2) is the energy used to cool or warm the subsurface soil. Since it is difficult to measure G at the regional scale, in this study it was estimated indirectly from the satellite-based net radiation, Rn. Many studies, employing remotely measurable variables in TIR and

The algorithms described in the previous paragraph were applied using a satellite-based stand-alone procedure, which exploits the potential of a set of time series products supplied by MODIS and MSGSEVIRI sensors. The remote sensing data from the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor on-board the Terra and Aqua satellites, covering, every 1–2 days, the entire earth's surface, can be retrieved from the Land Processes Distributed Active Archive Centre, LP DAAC, (http://lpdaac.usgs.gov/); these data have been used in this study for the estimation of regional ET and Λ (Eq. 2) (Table 1). The MODIS remote sensing data are composed of a land surface temperature/emissivity product (MOD11 A2) with a 1000 m spatial resolution, the broadband surface albedo (MCD43A3) and EVI (MOD13A1) products, with a 500 m spatial resolution. Both daytime and night-time products from MOD11 A2 are required in order to calculate the difference of diurnal and night-time land surface temperature, ΔTs. The albedo and EVI were obtained using 16-day composite datasets with a 500 m resolution from both Terra and Aqua sensors. The MODIS composite technique includes the determination of the two greatest albedo and EVI values for each pixel at the 16-day composite interval (Kim & Hogue, 2013). The 8-day phasing, included in the production of the 16-day composites between Terra and Aqua sensors, allows the generation of a combined 8-day time series of albedo and EVI. With these rules, in the examined study case, the number of selected MODIS/Terra and Terra/Aqua overpasses is of 104, between July 12th, 2010 (Day Of the Year — DOY 193) and November 16th, 2012 (DOY 321). The SEVIRI sensor on-board the Meteosat Second Generation (MSG) satellite allows ET estimation by including three short-wave channels

Fig. 6. Examples of standard “triangular feature space” obtained by plotting Ts vs EVI MODIS data for all pixels of Sicily (grey points) and three specific landuse classes at two different dates.

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Fig. 7. Time-domain based triangle feature space obtained for the orchard experimental site during the period of fluxes measurements (2010–2012): dependance of ΔTs-EVI values with the measured Priestley–Taylor ϕ coefficient (a) and DOY (b).

(0.6 μm, 0.8 μm, and1.6 μm) with 15 min acquisition intervals. As introduced in the previous paragraph, this enables to directly retrieve, by LSA-SAF, (http://landsaf.meteo.pt), the downward surface shortwave (RSS ↓, DSSF product, Level 1.5 SEVIRI/Meteosat) and longwave (RSL ↓, DSLF product, Level 1b SEVIRI/Meteosat) radiation fluxes (Table 1). The DSLF products were derived from a hybrid algorithm, which integrates cloud masks developed by the NWC-SAF (Nowcasting and Very Short-Range Forecasting, http://nwcsaf.inm.es/, Derrien & Gléau, 2005) and forecasts on atmospheric profiles, rainfall and near surface air temperature, provided by the European Centre for Medium-range Weather Forecasts (ECMWF). DIDSSF (LSA-09) and DIDSLF (LSA-12) SEVIRI products were averaged at the 8-day time-step for homogeneity with the MODIS dataset. Fig. 2 shows, for a typical day in July 2010, an example of 8-day averages of MODIS and MSG-SEVIRI products; these products were used in the study as sole inputs to estimate actual evapotranspiration. Fig. 3 shows the flow chart of the complete methodology herein proposed.

2.3. Study area, experimental sites and eddy covariance validation data The Sicily region, the largest island in the Mediterranean Sea, covers an area of approximately 26,000 km2, between coordinates 36°N to 38°N and 12°E to 15°E (Fig. 4a). The climate of the area is typically Mediterranean, with moderate rainfall during autumn and winter and high air temperatures and low precipitation in summer. The annual precipitation and temperature ranges between 350 and 1200 mm, and 4 and 36 °C, respectively. This variability is related to the different elevations and exposures, and as a consequence the island can be divided into four zones according to the De Martonne aridity index, from semi-arid to humid. The more humid area is located along the north coastal chain and on Mt. Etna, the highest European volcano (3350 m a.s.l.), whereas the more arid zones are located on the western part of Sicily and along the southern coast of the island. Semi-arid climate is characteristic of the hilly and lowland part of the island. In general, these areas are the most used

Fig. 8. Comparison between measured and estimated FC values obtained using Eq. (10) (panel a). Maps of FC obtained using eq. (10) for entire Sicily at different dates (panels b, c, d).

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Fig. 9. Temporal trends of measured Pristley-Taylor ϕ coefficients compared with TDTM estimations obtained using EVI and ΔTs MODIS time series. S.E.: standard error; M.E.: mean error.

for intensive agriculture. Land use and cover types are composed of arable (wheat, corn, sorghum, cotton), forest, grassland, water bodies (reservoirs and rivers) and urban areas (Fig. 4b). The TDTM approach, as previously described, was applied to estimate daily regional evapotranspiration during the 2010–2012 period in Sicily. The model results were validated by selecting two test sites located in the western and eastern parts of Sicily (Fig. 4c and d). The cropping systems (e.g. olive and orange orchards) of the two experimental areas are typical of the Mediterranean agricultural scenario and they substantially contribute to economy of the region. 2.3.1. Western Sicily test site 1 The experimental test 1, shown in Fig. 4c, has an area of about 13 ha and is cultivated with an olive orchard (cv. Nocellara del Belice). The site is located in the south-western part of Sicily (Italy), about 5 km from the town of Castelvetrano (37.6494″ N, 12.8492″ E, 123 m a.s.l.). The landscape is flat with a rather homogeneous soil type. The average tree

height was approximately 3.5 m and trees were spaced 5 × 8 m (density of 250 trees/ha), with an average fraction cover of 0.35. Water is supplied via drip irrigation (four 8 l h−1 emitter/tree). Soil hydraulic properties (i.e. soil water content at field capacity of 0.32 m3 m−3 and wilting point, of 0.08 m3 m−3) were analysed by laboratory methods. Soil textural class, according to USDA classification, is classified as silt clay loam. Sensible and latent heat flux (or evapotranspiration) measurements were conducted using the eddy covariance (EC) method (Rosenberg, Blad, & Verma, 1983; Kaimal & Finnigan, 1994; Stull, 1988; Cammalleri et al., 2013). A 4-components net radiometer (CNR-1 Kipp & Zonen) was positioned at an elevation of 6.5 m for net radiation direct measurements; two self-calibrated soil heat flux plates (HFP01SC, Hukseflux) were placed respectively in the exposed and shadowed bare soil, at a depth of about 0.1 m. The EC system allows for high frequency measurements of the three wind components (u, v, w), H2O and CO2 concentrations by means of a

Fig. 10. Time series variation of the satellite-derived net radiation (Rn, W m−2) during 2010–2012 compared with net radiation fluxes from EC at the two test sites in Sicily.

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Fig. 11. Comparison of net radiation (Rn, W m−2) observations from EC at the tower sites and the satellite-derived net radiation during 2010–2012.

three dimensional sonic anemometer (CSAT3-3D, Campbell Scientific Inc.) and an infrared open-path gas analyser (LI7500, Li-cor Biosciences Inc.), respectively. Both instruments were installed at a height of 7 m above the ground; the sample frequency for the high frequency EC data was 20 Hz. 2.3.2. Eastern Sicily test site 2 The test site 2, Figure 4d, is a 20-hectare orange orchard, planted with 20 year-old trees (Citrus sinensis, cv Tarocco Ippolito). The field is located in Lentini (Eastern Sicily, Lat. 37°16′N, Long. 14°53′E) in a Mediterranean semi-arid environment. The site is flat and presents large fetch conditions (i.e for the dominant wind directions, the fetch is longer than 550 m), which is satisfactory for micrometeorological measurements. Trees were spaced 4.0 m × 5.5 m and were drip irrigated with 4 in-line drippers per tree, with 4 l h−1 per dripper. The orange orchard shows the following mean features: canopy height of 3.7 m, average fractional cover of 0.65, mean leaf area index (LAI) of about 4 m2 m− 2, and mean PAR light interception of 80% within rows and 50% between rows (Castellví, Consoli, & Papa, 2012). Most soil textures (i.e. according to USDA standards) were loamy sand. The orange orchard was instrumented with an eddy covariance (EC) system (Rosenberg et al., 1983; Kaimal & Finnigan, 1994; Stull, 1988) mounted at a height of 8 m on a micrometeorological flux tower (Fig. 4d). Net radiation (Rn, W m− 2) was measured with two CNR 1 Kipp&Zonen (Campbell Scientific Ltd) net radiometers at a height of 6 m. Soil heat flux density (G, W m− 2) was estimated using three soil heat flux plates (HFP01, Campbell Scientific Ltd) placed horizontally, 0.05 m below the soil surface. Three different measurements of G were selected: in the trunk row (shaded area), at 1/3 of the distance to the adjacent row, and at 2/3 of the distance to the adjacent row. Table 2 Validation results for remote sensing estimates compared to observation at field sites in Sicily.

Ts RSS RSL Rn Rn − G ET

RMSE

Bias

Unit

R2

2.2 18.6 8.5 21.1 21.2 0.7

−0.74 2.5 −0.03 −8.1 −7.2 −0.4

K W m−2 W m−2 W m−2 W m−2 mm d−1

0.94 0.96 0.92 0.84 0.84 0.66

Fig. 12. Comparison of 2 m air temperature observations at the test sites and the corresponding satellite-derived value obtained by inversion of downward longwave LSA-SAF product.

The soil heat flux was measured as the mean output of three soil heat flux plates. Data from the soil heat flux plates were corrected for heat storage in the soil above the plates. The heat storage (ΔS) was quantified in the upper layer by measuring the rate of temperature change. The net storage of energy (ΔS) in the soil column was determined from the temperature profile taken above each soil heat flux plate. Three probes (TCAV) were placed in the soil to sample soil temperature. The sensors were placed 0.01–0.04 m (z) below the surface; the volumetric heat capacity of the soil Cv was estimated from the volumetric fractions of minerals (Vm), organic matter (V0) and volumetric water content (θ). Therefore, G at the surface was estimated by measuring G′ at a depth of 0.05 m and the change in temperature over time of the soil layer above the heat flux plates to determine ΔS. The air temperature and the three wind speed components were measured at 8 m, using fine wire thermocouples (CS FW3, 0.0762 mm diameter) and a sonic anemometer (CSAT, Campbell Sci., at 8 m). An infrared gas analyser (LI-7500, LI-COR) was installed at 8 m for H2O and CO2 acquisition. The high frequency EC data were recorded at 20 Hz. 2.3.3. Eddy covariance measurements The standard EUROFLUX rules (Aubinet et al., 2000) were adopted for eddy covariance measurements and data processing. Common errors in the measured high frequency data, such as running means for detrending, three angles coordinate rotations and despiking, were removed during the post processing by quality checks. The stationary of the surface flux layer and the surface energy balance closure were also evaluated (Kaimal & Finnigan, 1994). Eddy Covariance sensible heat flux H (W m−2) was computed as: H ¼ ρ  cp  σ wT

ð16Þ

where ρ (g m−3) is the air density, cp (J g−1 K−1) is the air specific heat capacity at constant pressure and σwT (m s−1 K) is the covariance between the vertical wind speed and air temperature. The vertical flux of water vapour content, i.e. the latent heat flux (λET, W m−2), was expressed as: λET ¼ λ  σ wq

ð17Þ

where λ (J g−1) is the latent heat of vaporization and σwq (m s−1 K) is the covariance between the vertical wind speed and water vapour concentration.

M. Minacapilli et al. / Remote Sensing of Environment 174 (2016) 10–23

19

Fig. 13. Time series of the modelled evapotranspiration (ET, mm d−1) during July, 2010 and November, 2012 for the two test sites.

The surface energy balance closure ratio is expressed as: CR ¼

ðH þ λETÞ ðRn −GÞ

ð18Þ

and allows for the determination of how well the turbulent fluxes of heat and water vapour account for the available energy. The ratio, as suggested by Prueger et al. (2005), was performed only when Rn is greater than 100 W m−2. Thirty-minute fluxes data were aggregated to a daily scale and latent heat fluxes, acquired in W m−2, were then transformed to equivalent depth of ET (mm d−1). In both the test sites, hourly meteorological data (incoming shortwave solar radiation, air temperature at 2 m, atmospheric pressure, air humidity, wind speed and rainfall) were acquired by two automatic weather stations located about 7 km from the orchard sites and managed by SIAS (agro-meteorological service of the Sicilian region). To ensure homogeneity with the satellite dataset, for both the test areas, daily mass and energy fluxes measured by the EC system were aggregated at 8-day average and only the corresponding data to the satellite time were used. The scatterplot of Fig. 5 shows the closure of the hourly energy measured fluxes.

Fig. 14. Measured vs. modelled actual evapotranspiration ET at the test sites.

The freely distributed TK2 package (Mauder & Foken, 2004) was used to determine the first and second order statistical moments and fluxes on a half-hourly basis following the protocol used as a comparison reference described in Mauder et al. (2007). This software corrects for the errors in the wind speed vertical components, sensor separation and path-length averaging, density effects due to heat and water vapour transfer (WPL) and eliminates spurious flux values. The micrometeorological dataset, used for comparison, included samples (of high and low frequency data) that passed the Foken's quality control test up to level 7 (Mauder & Foken, 2004). The test checks the assumptions of steady flow and developed turbulence invoked in the EC method. Then, variances and covariances are discriminated in levels of reliability. Up to level 7 (i.e. from 1 to 7), the dataset includes high quality flux measurements recommended for research purposes (up to level 3) and measurements that can be considered useful for routinely applications and gap filling (from 4 to 7). The range −20 Wm−2 ≤ HEC ≤ 20 Wm−2 was excluded (taken as the EC measurement error) (Foken, 2008). 3. Results and discussion In this paragraph the application of the TDTM using MODIS and MSG-SEVIRI time series products, for the period 2010–2012, is discussed. In the first two parts of the results (Sections 3.1 and 3.2), we examined the performance of the TDTM approach to derive the Priestley–Taylor ϕ parameter (Eqs. (7), (8) and (9)). In the last two parts (Sections 3.3 and 3.4), we compared satellite-based estimates of

Fig. 15. Spatial distribution of land surface temperature day-night differences obtained from MODIS data during the period 2010–2012.

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M. Minacapilli et al. / Remote Sensing of Environment 174 (2016) 10–23

Fig. 16. Satellite derived actual evapotranspiration map (mm d−1) at different dates.

net radiation, Rn, and evapotranspiration, ET, versus ground measurements at the flux tower sites. 3.1. Validation of the TDTM conceptual basis by means of ground observations To clarify the conceptual basis of the TDTM, a standard determination of the triangle method was performed, considering only the spatial domain of two selected time scenes; these scenes were chosen from two typical periods (i.e. March 22nd 2011 was the end of rainy period and August 25th 2011 was the end of the dry season) of the annual seasonal Mediterranean climate. For these two scenes, Fig. 6 shows the corresponding standard “triangular feature space” obtained by plotting ΔTs versus EVI MODIS data for all pixels of Sicily (grey points) and for two different land-use classes. Fig. 6 shows how the clusters pixels with the same crop types change in time their position within the triangle, following the so-called “temporal trajectories” described by Carlson (2007). Therefore, even if in Fig. 6, a general triangle shape is easily recognizable for each date, each identified land-use class is characterized by a univocal cluster and, as consequence, specific warm and cold edges, for land uses, can be observed. Moreover, from Fig. 6 it is clear that the idea of the classical application of the triangle method is useful only in a specific instant of time, when using the atmospheric homogeneity requirement. In contrast, for each observation, the TDTM provides the time series estimation, by adopting a unique parameterization, which requires the min/max MODIS products of ΔT and VI for each pixel. An example of TDTM scatterplot is shown in Fig. 7, where ΔTs and EVI data, acquired from MODIS sensor, are plotted for the test site 2 (orange orchard), when EC fluxes measurements were available for the period 2010–2012. Fig. 7a-b shows in greater detail the dependence of ΔTs-EVI data to the measured Priestley–Taylor ϕ coefficient changes. Experimental data, scattered over the ΔTs vs EVI space, can be assimilated to a triangular shape, indicating the presence of two boundaries between a minimum (ϕi b 1) and maximum evapotranspiration (ϕi N

1.26). In the upper boundary of the scattering, similarly to the standard triangle method, measured data points delineate the warm edge, whereas data points posed on the lower boundary identify the maximum evapotranspiration condition or cool edge. Additionally, these two edges are coherent with the expected seasonal dynamics of the study areas; in fact, flux measurement collected during DOYs 100–250 (mid April to September early) are located closer to the warm edge; conversely, scattering on cold edge mainly consists of flux measurements collected during DOYs 0–100 (January to mid-April) and 250– 360 (September to December). The first period corresponds to the highest atmospheric water demand with high temperature and limited soil water availability, causing lowest ϕi values (0.8–1.0). The opposite atmospheric conditions characterize the second period, localizing the corresponding data points near to the cold edge. Moreover, within the triangle space, for a given ground cover condition in terms of EVI value, the experimental data scattering follows, in terms of both ΔTs and ϕ values, the seasonal variability expected under Mediterranean climate conditions. In particular, during the summer dry season (DOYs 150–240), without spontaneous vegetation ground cover and lower EVI values (0.35), fully ascribed to orange tree canopy, the dynamic of the measured ϕi values follows the changes in surface temperatures, according to the typical seasonal pattern, i.e. lowest ϕi values at the peak of dry season (DOYs 210–230) and highest ϕi values in the summer-autumn transition (DOYs 150–270). These preliminarily results confirm the feasibility of using the set of Eqs. (7), (8) and (9) to compute the Priestley–Taylor ϕ coefficient from a time series of ΔTs and EVI derived through satellite measurements. 3.2. Modelling and validation of the Priestley–Taylor ϕ coefficient using the TDTM As described in the methodology section, the TDTM-based ϕ coefficient calculation requires a preliminary estimation of the fractional cover, Fc (Eq. 9). To this aim, using a set of fractional cover measurements obtained in eight test areas of Sicily, covering various land types representing a wide range of natural and agricultural ecosystems,

M. Minacapilli et al. / Remote Sensing of Environment 174 (2016) 10–23

a specific calibration of the “b” exponent of Eq.(9) was performed. As shown in Fig. 8, in fact, a constant “b” value of 0.46 was able to describe the variation of Fc over the entire region. Particularly, the comparison between estimated vs. measured Fc values (Fig. 8a) was linear over the explored range (0.2 b Fc b 1.0) of land types. Fig. 8(b, c, d) shows an example of the Fc spatial distributions at three different dates. Finally, the set of Eqs. (7), (8) and (9), of the TDTM approach, was applied using MODIS LST and EVI products as input. The outputs, referred to the two test sites, were compared with the corresponding measurements obtained by inverting the Priestley–Taylor's equation, with the EC fluxes data as input (Fig. 9). As reported in Fig. 9, the TDTM-based ϕ estimates vs. EC-observed values showed similar dynamics along the observation period. The ϕ values ranged from 0.5 to 1.5 in both test sites, with an acceptable agreement of estimated and measured values during most (80%) of the dates. Some significant differences were observed during winter and spring-time periods, when measured ϕ values were higher than those modelled. This circumstance may depend on a slight decrease of both EC fluxes and MODIS data quality, mainly due to rainfall events or greater cloud cover conditions. In any case, the discrepancies between observed vs. modelled ϕ values were most evident during periods of low available energy (Rn − G), with less impact on evapotranspiration fluxes estimation. During the dry seasons, when crop water demand is higher, the TDTM estimates of ϕ values fit well with the corresponding observed values. To conclude, the general performance of the proposed TDTM procedure is acceptable for practical applications, as confirmed by the statistical comparisons between measured and estimated ϕ values, reporting standard errors (S.E.) of 0.17 and 0.27 and medium errors (M.E.) of −0.04 and −0.07 for orange and olive groves, respectively.

3.3. Modelling and validation of net radiation and soil heat flux The total energy available (Rn − G) is a key variable in estimating ET. In the study, the comparison between measured and modelled net radiation (Rn, W m−2) (Eqs. (10) and (15)), at the satellite overpass time, is illustrated in Figs. 10 and 11, with the associated statistics listed in Table 2. At both the test sites, the time series of modelled Rn, estimated from the combination of MODIS (albedo, land surface temperature and surface emissivity) and MSG-SEVIRI (RSS↓ and RSL↓), and the ground measured Rn were a good agreement (Fig. 10). The scatterplot of modelled vs ground-measured Rn was linear (Fig. 11), with R2 of 0.85 and RMSE of 21.1 W m−2, corresponding to 17% of the measured mean Rn. Soil heat flux, G, showed a smaller variability compared to the measurements and a RMSE of 4.7 W m−2. The modelled mean daytime available energy term, Rn − G had a RMSE of 21.2 W m−2, a bias of −7.2 W m−2 and R2 of 0.84, when compared with field observations. The relatively high RMSE and bias values reported in Table 2 are ascribed to systematic biases that can be detected in well-defined time-windows (for example from April to July 2011). It is important to notice that an improvement on Rn estimation could be achieved by analysing each single remote sensing product, its role and impact on the estimation equation, given the systematic nature of the observed errors. As an example, biases of opposite signs were observed at the two sites, characterized by quite different tree crops species, cultivation methods and irrigation supplying, which differences are not entirely detectable at moderate scale resolutions. Another source of error might consist on the different original temporal resolution of MSG-SEVIRI (i.e. daily data, Table 1) and MODIS products (8-day data, Table 1). However for operational purposes, the obtained RMSE and biases can be considered acceptable, taking into account also that Rn was exclusively estimated using remote sensing products, without ancillary ground based data.

21

3.4. Modelling and validation of evapotranspiration by the TDTM The use of the Priestley–Taylor equation to estimate actual ET data requires the meteorological parameters Δ and γ (i.e. easily computed using Eqs. (3) and (4)), air temperature, Tair, and elevation, z (m) as input. In our case, for the Sicily region, the elevation z was derived by the use of a digital elevation model, (DEM), and the inversion of Eq. (12) was applied to estimate Tair as:  Tair ¼

RSL↓ εallsky σ

1=4 ð19Þ

where RSL↓ is the downward longwave radiation LSA-SAF product and εallsky is the atmospheric emissivity computed using Eq. (13). Fig. 12 shows a preliminary validation of the procedure with regard to the ground based measurements at the two test sites. Measured and estimated air temperature, Tair, data result in a good agreement, as reported in Fig. 12. This approach provides air temperature maps using LSA-SAF products in terms of both spatial and temporal resolutions. For the two test sites, measured and modelled actual ET time-series matched well, with a bias of − 10.9 W m− 2, R2 of 0.66 and RMSE of 21.3 W m−2 (Table 2 and Fig. 14). A detailed analysis of Fig. 13 shows some underestimation of ET for the orange orchard (test site 2) during the fall-winter period (for 2010 and 2012). Considering that in these periods Rn is well modelled (see Fig. 10), this underestimation, as confirmed by Fig. 9, can be ascribed to the modelled ϕ values. This poor model performance could be related to the quality of MODIS products during the fall-winter period as previously described. However, being the described methodology developed without a specific calibration, the obtained results can be considered satisfactory. Moreover, the proposed TDTM approach, applied on 99 validation days (29 days from the olive orchard test site and 70 days from the orange orchard test site) within 3 consecutive years, can be considered as robust. In the definition of the spatial distributed ET data, the key-step consists on the spatial-temporal assessment of the Priestley–Taylor ϕ parameter, which is based on the dynamics of the normalized day-night surface temperature term of Eq. (8); the major component of this term is the normalization step, which is computed as: NTsi; j ¼ ΔTsi: j; max −ΔTsi; j; min :

ð20Þ

Fig. 15 shows the spatial distribution of the NTs term, estimated using MOD11A2 surface temperature time-series over the period 2010–2012. The well-defined spatial patterns of NTs over Sicily can be related to a combined effect of atmospheric, morphological and surfaces conditions (Fig. 4b), denoting the typical “ecological faces” of Sicily. In particular, the higher NTs values occurring in the inland areas of Sicily depend on the cover type, consisting of winter cereal crops with a strong seasonality pattern in Fc (highest values in winter and zero in summer), associated with the geographic location (inland site whit highest daily temperature variation). On the contrary, the lower NTs values are observed in the northern coastal side of the island, where ever green tree species (both crops and forest) are dominant. In these conditions, the seasonal changes of daily temperature are expected to be minimal due to the mitigation effect of sea, combined to ever-green vegetation cover. The ability of the NTs term to take into account the combined effect of atmospheric, morphological and surfaces conditions can be considered as useful to compensate for some of the assumptions of the classic triangle method approach, i.e. homogeneous atmospheric condition over the spatial domain. Finally, distributed maps of daily ET were produced. Such maps, illustrating the spatial pattern of ET fluxes for three typical seasonal

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conditions (end of rainy season, spring time and end of dry season), are presented in Fig. 16. The ET spatial distribution shows typical values, such as: i) at the end of rainy season (03.30.2011, Fig. 16a), ET ranged from 0 to 3.5 mm d−1, with highest values in the inland part of region, characterized by arable land covered at full canopy development and the highest seasonal soil water availability; ii) at spring time (05.25.2011, Fig. 16b), when the maximum range of ET occurred (0–7 mm d−1), with highest values in the northern coastal area of the island, which gradually decrease moving to the internal drier zones; iii) in summer (08.03.2011, Fig. 16c), when ET values ranged from 0 to 4 mm d−1, with highest values in a limited portion of the northern coastal area, and lowest values in internal drier areas. 4. Conclusion and future remarks In this study, a time-domain (TDTM) parameterization of the traditional “triangle method” was proposed to estimate actual evapotranspiration at regional level; the approach was tested in a typical Mediterranean environment (insular Italy). The research was motivated by the recent availability of time-series of satellite products provided by NASA and EUMETSAT. The combined use of these products allowed to identify a new methodology to derive the boundaries of the Ts–VI feature space proposed by Stisen et al. (2008), which are necessary for the correct parameterization of the Priestley–Taylor coefficient. The comparison between actual evapotranspiration rates, modelled by the proposed TDTM model, and the corresponding measurements by eddy covariance systems showed a satisfactory agreement, with standard error of about 0.6 mm d−1. The major key-points of the proposed TDTM can be summarized as in the follows: • The TDTM is based on a “temporal domain”, obtained from the standard time series of MODIS products (LST and VIs); • The TDTM eliminates the requirements of uniformity in atmospheric conditions, and, by the length of the time series, satisfies the need for a high number of pixel to better define the triangle edges. Theoretically, the boundary conditions parameterization is realized by exploring the temporal variability of LST and VIs pixel by pixel, whose fluctuations intrinsically contain the variability of surface atmospheric conditions. • The TDTM method results are completely independent from ancillary ground-based measurements (i.e. through EUMETSAT products).

Further research aiming at developing and refining the proposed TDTM method, might include: ▪ an automatic pre-elaboration procedure to take into account the quality index of MODIS products; ▪ a finer temporal resolution of MODIS data (i.e. daily time series, instead of 8-day time series); this, of course, would imply higher computational efforts and data preparation; ▪ the use of the Fluxnet database, regarding micrometeorological mass and energy fluxes, in order to validate the proposed TDTM approach over a wider environmental scenarios; ▪ the direct use of the original atmospheric emissivity data, included in the MSG-SEVIRI product, would improve the TDTM method performance.

Acknowledgments Research funded by the Ministry of University Research and Education (MIUR) Project PRIN 2010–2011 — titled “Traditional agricultural landscapes in Italy: multi-disciplinary and multi-scale assessment for

the development of an integrated model for landscape planning and management” (Prot. 2010LE4NBM).

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