Surv Geophys (2010) 31:531–555 DOI 10.1007/s10712-010-9102-2

Vegetation Index Methods for Estimating Evapotranspiration by Remote Sensing Edward P. Glenn • Pamela L. Nagler • Alfredo R. Huete

Received: 6 June 2010 / Accepted: 20 September 2010 / Published online: 17 October 2010 Ó Springer Science+Business Media B.V. 2010

Abstract Evapotranspiration (ET) is the largest term after precipitation in terrestrial water budgets. Accurate estimates of ET are needed for numerous agricultural and natural resource management tasks and to project changes in hydrological cycles due to potential climate change. We explore recent methods that combine vegetation indices (VI) from satellites with ground measurements of actual ET (ETa) and meteorological data to project ETa over a wide range of biome types and scales of measurement, from local to global estimates. The majority of these use time-series imagery from the Moderate Resolution Imaging Spectrometer on the Terra satellite to project ET over seasons and years. The review explores the theoretical basis for the methods, the types of ancillary data needed, and their accuracy and limitations. Coefficients of determination between modeled ETa and measured ETa are in the range of 0.45–0.95, and root mean square errors are in the range of 10–30% of mean ETa values across biomes, similar to methods that use thermal infrared bands to estimate ETa and within the range of accuracy of the ground measurements by which they are calibrated or validated. The advent of frequent-return satellites such as Terra and planed replacement platforms, and the increasing number of moisture and carbon flux tower sites over the globe, have made these methods feasible. Examples of operational E. P. Glenn (&) Environmental Research Laboratory of the University of Arizona, 2601 East Airport Drive, Tucson, AZ 86706, USA e-mail: [email protected] P. L. Nagler U.S. Geological Survey, Southwest Biological Science Center, Sonoran Desert Research Station, University of Arizona, 1110 E. South Campus Drive, Room 123, Tucson, AZ 85721, USA e-mail: [email protected] A. R. Huete Department of Soil, Water and Environmental Science, University of Arizona, Tucson, AZ 86721, USA e-mail: [email protected]; [email protected] A. R. Huete Plant Functional Biology and Climate Change Cluster, University of Technology, Sydney, NSW, Australia

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algorithms for ET in agricultural and natural ecosystems are presented. The goal of the review is to enable potential end-users from different disciplines to adapt these methods to new applications that require spatially-distributed ET estimates. Keywords

NDVI  Enhanced Vegetation Index  Fluxnet  MODIS  Remote sensing

1 Background 1.1 Need for Remote Sensing Estimates of ET Estimates of terrestrial evapotranspiration (ET) are needed for land management tasks at local, regional and continental scales of measurement, and to project potential changes in the global hydrological cycle under different climate change scenarios (e.g., Allen 2005; Teuling et al. 2009). Remote sensing is perhaps the only feasible means of estimating ET over wide areas of mixed landscape types, typical of applications for which regional water budgets are required. Some of the specific tasks for which remote sensing estimates of ET are used are: determining consumptive water use by crops in irrigation districts, to construct district-wide water budgets (e.g., United States Bureau of Reclamation 2009); refining crop coefficients for individual crops to match local conditions (e.g., Hunsaker et al. 2007); characterizing water use patterns of plants in natural ecosystems in ecological studies (e.g., Groeneveld et al. 2007; Dennison et al. 2009); developing wide-area estimates of ET to construct catchment water budget models (e.g., Guerschman et al. 2009); and scaling flux tower measurements of ET and carbon exchange over biomes and continents, to be used in climate change studies (e.g., Leuning et al. 2008; Fisher et al. 2008). In most of these applications, time-series satellite imagery is used to project ET over spatial and temporal scales that cannot be achieved by point estimates of ET measured on the ground. 1.2 Thermal Band and Vegetation Index Approaches to Estimating Evapotranspiration The most common approaches to estimating ET by remote sensing have utilized thermal infrared (TIR) (ca. 8–14 lm wavelength) sensors on satellites (Kustas and Norman 1996; Kalma et al. 2008; Courault et al. 2005). These methods are based on solving a simplified form of the surface energy balance (SEB) equation: LE ¼ Rn  H  G

ð1Þ

where LE is the latent heat of evaporation due to ET; Rn is net radiation absorbed by the land surface, equal to incoming solar radiation (Rs) minus outgoing shortwave and longwave radiation; H is sensible heat flux to the atmosphere; and G is heat flux to the soil. In this equation variables are expressed in energy units (W m-2). ET in volume units (e.g., liters m-2 d-1, usually simplified to mm d-1 to express ET as a depth of water over an indefinite area) can be calculated from LE by the amount of energy needed to evaporate water at a given temperature and pressure. If heat transfer coefficients are known or can be estimated, H can in theory be calculated from the difference between air temperature at some reference height and the land surface temperature (LST), measured by TIR bands on satellites such as the Landsat series (e.g., Bastiaanssen et al. 2005; Allen et al. 2007; Kustas and Anderson 2009), Geostationary

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Operational Environmental Satellite (GOES) (Diak et al. 2004), the Advanced Very High Resolution Radiometer series (Brown et al. 1993), the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) (McCabe and Wood 2006), and the Moderate Resolution Imaging Spectrometer (MODIS) sensors, both on the Terra satellite (Nishida et al. 2003a, b). Estimates of Rn and G are available from remote sensing or ground data, allowing LE to be calculated as a residual in Eq. 1. Numerous SEB approaches to ET have been developed since the feasibility was first suggested by Jackson et al. (1977, 1983). The problems encountered in developing SEB methods and approaches to surmounting them have been reviewed recently (Diak et al. 2004; Courault et al. 2005; Glenn et al. 2007; Kalma et al. 2008; Verstraeten et al. 2008; Kustas and Anderson 2009; Petropoulos et al. 2009; Tang et al. 2009). Although approaches differ, several of the methods have been validated by comparison with moisture flux tower stations in a variety of landscapes and are considered operational (e.g. Bastiaanssen et al. 2005; Gonzalez-Dugo et al. 2009; Kustas and Anderson 2009; Allen et al. 2007). SEB methods generally have an error or uncertainty factor of 10–30%, which is within the range of error or uncertainty of the ground ET methods by which they are validated (Courault et al. 2005; Jiang et al. 2004; Kalma et al. 2008). SEB methods have been preferred by the atmospheric science community because they are based on measurement of a physical property of the surface (LST) that is directly related to LE through Eq. 1 (Overgaard et al. 2006). By contrast, vegetation index (VI) methods are indirect (Glenn et al. 2007; Kalma et al. 2008). They depend on an estimate of the density of green vegetation over the landscape, as measured by VIs or related products that use combinations of visible and near infrared (NIR) (ca. 850 nm wavelength) bands (Bannari et al. 1995; Huete et al. 2002; Glenn et al. 2008a, b). Most VIs ratio the reflectance of light in adjacent Red and NIR bands, to provide a measure of absorption of red light by chlorophylls a and b and reflectance or scattering of NIR by cell wall constituents and the well-structured layers of leaf cells in canopies. VIs are an integrated product of LAI, chlorophyll content, leaf angles, fractional cover and canopy architecture over vegetated surfaces (Nagler et al. 2004; Glenn et al. 2007, 2008a, b). Several early studies showed that VIs are nearly scale-invariant in going from leaf-level ground measurements, to aerial measurements, then to large-area satellite measurements (Hall et al. 1992; Hall and Sellers 1995). They are strongly correlated with physiological processes that depend on photosynthetically active radiation absorbed by a canopy (APAR), such as transpiration and photosynthesis (Sellers 1987; Sellers et al. 1992). However, VI methods cannot estimate bare soil evaporation or differences in stomatal conductance among species and as affected by environmental factors, and these must be approximated from ground data or additional remote sensing data. 1.3 Need for VI Methods The purpose of this review is to describe VI methods for ET, not to compare them in detail with the more traditional TIR methods. However, this section presents some background on why new VI methods have been developed over the past 5 years. The need for alternative ET methods has been highlighted in a number of recent studies (Nagler et al. 2005a; Cleugh et al. 2007; Mu et al. 2007; Fisher et al. 2008; Leuning et al. 2008; Guerschman et al. 2009). A primary motivation for developing VI methods appears to be that SEB methods have been difficult to implement using MODIS, which has become a primary source of

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Earth-observing data since the launch of Terra in 1999 (Running et al. 2004; Pan et al. 2006). Nishida et al. (2003a, b) developed a simple two-source method for ET based on MODIS VIs and LSTs, which they described as ‘‘operational’’. However, it was not subsequently offered as a validated MODIS science product. More recently, Tang et al. (2010) reported successful application of the triangle SEB method using cross plots of MODIS VIs and LSTs when they used daily values rather than the composite 8 or 16 day standard LST products. However, Nagler et al. (2005a) found no correlation between ET and Ta - LST (the starting point of many SEB methods) using MODIS LST products in southwestern US riparian corridors, whereas a strong relationship was found between vegetainetion indices * air temperatures and ET. Scott et al. (2008) and Wang and Liang (2008) reported that LST could be used as a proxy for air temperatures in empirical VI methods, but was not useful in solving Eq. 1 to calculate ET. Cleugh et al. (2007) compared MODIS-based SEB and VI methods against ground measurements of ET over 3 years in evergreen forest and savanna ecosystems in Australia. The SEB methods failed because small errors in LSTs translated into large errors in estimates of H in Eq. 1, and hence into large errors in estimating ET. By contrast, the VI model adequately estimated the magnitude and seasonality of ET in both ecosystems. McCabe and Wood (2006) reported that MODIS LSTs were unable to discriminate the heterogeneity of ET at the field scale over Iowa, USA, croplands, due to low pixel resolution. Similarly, Su et al. (2007) reported RMSEs of 61–141 W m-2 comparing MODIS SEB estimates of ET with tower measurements at eight sites distributed over different landscape types around the world, with RMSEs up to 50% of mean values. Low accuracy was attributed to the low spatial resolution of LST measurements, leading to erroneous ET estimates in heterogeneous landscapes. Hence, operational ET methods based on MODIS data tend to use VI methods as described in Section 3.5. Additionally, the number of satellite sensors that have TIR bands is limited, due to the difficulty and expense of building the sensors and maintaining them in the space environment. There might be a gap in TIR coverage in the Landsat series of satellites due to failure of the Landsat ETM ? data acquisition system, and lack of a replacement satellite until 2012 or latter (Allen et al. 2005). After that, the next potential new source of moderate resolution TIR data will be NASA’s Hyperspectral and Infrared Imager (HyspIRI), which is still in the study stage and might not be launched until 2017 (Hook and Oaida 2010). By contrast, there are quite a number of satellites with bands in the visible and NIR range needed to calculate VIs over a wide range of temporal and spatial resolutions, and it is relatively straightforward to inter-calibrate VI values among sensors using empirical methods or physical models, with a potential accuracy of 1–2% (Stevens et al. 2003). Therefore, now is a good time to examine VI approaches to ET estimation. 1.4 Purpose of the Review This review examines the utility of VI approaches to ET estimation based on studies conducted in agricultural and natural biomes, with an emphasis on recent studies. The goal is to describe the new methods and their applications in sufficient detail that they can be adapted more widely by end-users to new land management applications. We also discuss the limitations of VI approaches, and in a final section, we suggest that maximum information about the landscape can be obtained by combining modeling, ground and remote sensing approaches rather than attempting to develop stand-alone remote sensing products.

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2 VIs and Related Products Used in ET Studies The Normalized Difference Vegetation Index (NDVI) is the most commonly used VI. It is calculated as: NDVI ¼ ðqNIR  qRedÞ=ðqNIR þ qRedÞ

ð2Þ

where qNIR and qRed are the reflectance values received by a sensor over a vegetated surface. NDVI values fall between -1.0 and ?1.0, with water having negative values, soil slightly positive values, and vegetation having increasingly high values approaching 0.9 for dense vegetation cover (Bannari et al. 1995). Two other VIs used in the ET studies reported here are the Soil Adjusted Vegetation Index (SAVI) and the Enhanced Vegetation Index (EVI) (Nagler et al. 2001; Huete et al. 2002). SAVI is calculated as: SAVI ¼ ðqNIR  qRedÞð1 þ LÞ=ðqNIR þ qRed þ LÞ

ð3Þ

where L is a correction factor usually set at 0.5 to account for soil effects. EVI is calculated as: EVI ¼ GðqNIR  qRedÞ=ðqNIR þ C1  qRed þ C2  qBlue þ LÞ

ð4Þ

where C1 and C2 are coefficients designed to correct for aerosol resistance, which uses the blue band to correct for aerosol influences in the red band. C1 and C2 have been set at -6 and 7.5, while G is a gain factor (set at 2.5) and L is a canopy background adjustment (set at 1.0). These VIs are described in detail in (Huete et al. 2002). EVI and SAVI are non-linearly related to NDVI (Fig. 1) and extend the range over which VIs respond to increases in foliage density (Choudhury et al. 1994; Nagler et al. 2001; Huete et al. 2002). Related to NDVI is the MODIS Leaf Area Index (LAI) product (Myneni et al. 2002) used in some ET studies. It uses visible and NIR data collected at several view angles and tabular data on land cover type to calculate LAI based on a radiation transfer model. There is a strong but non-linear relation between MODIS LAI and NDVI products, and NDVI is used to fill in data gaps when the complete LAI algorithm cannot be implemented.

3 VI Methods for Agricultural Crops 3.1 The Crop Coefficient Approach to ET Equation 5 is the basis for the widely used, crop-coefficient method for estimating actual ET (ETa) of crops (Allen et al. 1998): ETa ¼ Kc ETo

ð5Þ

where Kc is a coefficient for a particular crop at a given state of development, determined by growing crops in precision weighing or drainage lysimeters under typical field conditions, and ETo is the theoretical ET of a hypothetical, unstressed reference crop, determined from meteorological data. Crop coefficients change (typically monthly) over a crop cycle according to the developmental stage of the crop. ETo is calculated by automated micrometeorological stations distributed within agricultural districts. Monthly estimates of ETa from Eq. 5 are used to determine irrigation schedules, to avoid under- or overirrigating crops, and in estimating irrigation district water budgets (e.g., United States

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Fig. 1 Relationship between Normalized Difference Vegetation Index, Soil-Adjusted Vegetation Index and Enhanced Vegetion Index for 64 riparian sites in the Colorado River delta, Mexico. Vegetation indices were calculated from reflectance values recorded by a multi-band digital camera using high-resolution aerial photography (from Nagler et al. 2001)

Bureau of Reclamation 2009). Crop coefficients are often adjusted for local conditions based on expert opinion or experimentation within an irrigation district (e.g., Jensen 1998). ETo formulas range from the simple to the complex, but usually produce values within 5–10% of each other when calibrated to local conditions (Xu and Shen 2005; Xu and Singh 2002). The Penman–Monteith equation for ET is generally preferred in agricultural applications because it includes all the main environmental variables affecting ET as well as stomatal and canopy conductance terms related to plant physiological status and architecture (Monteith and Unsworth 1990). Expressed as the latent heat of evaporation (LE), the general Penman–Monteith formula is:
ð6Þ LE ¼ ðDRn  GÞ þ qa cp ðes  ea Þ=rs =ððD þ cð1 þ rs =ra ÞÞ where (es-ea) represents the vapor pressure deficit (VPD) of air, qa is the mean density of air at constant pressure, cp is the specific heat of the air, D represents the slope of the VPD temperature relationship, and c is the psychometric constant (ratio of the specific heat of the air to the latent heat of water vapor). The term es is the moisture content of the air over the canopy at saturation and it is calculated from D and air temperature (Ta); ea is the actual water content of the air over the canopy. The term rs is the resistance to vapor flow from the soil and transpiring vegetation surfaces in the canopy; it is related to soil moisture content and soil resistance to water transport (for E from the soil), and plant leaf area index (LAI) and stomatal resistances (for T from the canopy). The term ra is the resistance of vapor flow from the canopy into the air above the canopy; it is related to the height and

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architecture of the canopy and the wind speed over the canopy. ETo is then calculated in daily time steps using assumed values for the crop-dependent terms in Eq. 6. The United Nations Food and Agriculture Organization (FAO) has defined a standard reference surface for calculating ETo as: ‘‘A hypothetical reference crop with an assumed crop height of 0.12 m, a fixed surface resistance of 70 s m-1 and an albedo of 0.23’’ (Allen et al. 1998). Albedo is needed to calculate Rn from Rs. 3.2 Improving the Crop Coefficient Method by Including VIs Bausch and Neale (1987, 1989) showed that VIs could increase the accuracy of crop coefficients by providing a measurement of the actual state of the crop canopy during development. Choudhury et al. (1994) explored the theoretical basis of using VIs to replace Kc in Eq. 5. Using wheat as a model crop, they showed that: Tc ¼ ðVIÞg

ð7Þ

where Tc is a plant transpiration coefficient (by analogy with Kc) and VI* is a vegetation index stretched between 0 (representing bare soil) and fully transpiring, unstressed vegetation, using the formula: VI ¼ 1  ðVImax  VIÞ=ðVImax  VImin Þ

ð8Þ

VImax and VImin are determined from satellite image statistics for individual scenes (e.g., Groeneveld et al. 2007), large data sets encompassing a wide range of VI values (Nagler et al. 2005a, b), or from radiometric measurements of crops grown in lysimeters (e.g., Hunsaker et al. 2005a, b). Then ETa (ignoring bare soil evaporation) is approximated as: ETa ¼ ETo ðVIÞg

ð9Þ

The exponent, g, is determined by the relationship between transpiration and the VI used in Eq. 7. Choudhury et al. (1994) pointed out that SAVI (and by extension EVI from which it is derived) extends the range of leaf area index (LAI) values over which a VI is responsive, because it does not ‘‘saturate’’ as quickly as NDVI at high LAIs (see Fig. 1). They showed that SAVI was curvilinearly related to LAI up to LAI 5, and since ET is also curvilinearly related to ET, ET was near-linearly related to SAVI. Hence, for EVI and SAVI, the exponent g in Eq. 7 is 1.0. By contrast, NDVI saturated at an LAI of about 3.0, was curvilinearly related to ET, and g was less than 1.0. SAVI also had a higher r2 relationship to measured ET than NDVI. Choudhury et al. (1994) also noted that Eq. 7 could be applied across different crop types while still maintaining a high correlation (r2 = 0.80) between measured ET and calculated ET. This is important because most satellite sensor systems cannot distinguish between different crops. 3.3 Applications of VI Methods in Agriculture Variations of Eq. 9 have been applied to a number of crops for which accurate, weighing lysimeter values of ET are available. Using hand-held radiometers, high-resolution digital aerial imagery, or satellite imagery, NDVI-based crop coefficients have been developed for cotton (Hunsaker et al. 2005a, b), wheat (Hunsaker et al. 2005a, b; Er-Raki et al. 2010), potato (Jayanthi et al. 2007), corn (Bausch and Neale 1987, 1989; Bausch 1993, 1995), broccoli (El-Shikha et al. 2007) and other crops (e.g. Neale et al. 2005; Gonzalez-Dugo et al. 2009; Papadavid et al. 2009; Singh and Irmak 2009).

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Work with irrigated wheat grown in an arid-zone irrigation district in Arizona in the U.S. provides an example of the successful application of these methods (Hunsaker et al. 2005a, b, 2007). First, a model for wheat ET based on ETo and NDVI was developed, which predicted ET with less than a 5% error compared to lysimeter values (Hunsaker et al. 2005a, b). The model was based on the expanded FAO-56 method for estimating ETa, which includes a basal crop coefficient, Kcb, identical to Tc in Eq. 7, and a separate term, Ke, that accounts for soil evaporation: ETa ¼ Kcb ETo þ Ke ETo

ð10Þ

Ke is estimated from models of the soil drying curve following a rainfall or irrigation event, based on soil type and depth of water (Allen et al. 2005). In these studies it was approximately 10% of ETa. Wheat was then grown in replicated field plots for two seasons under four treatment combinations: sparsely planted and nitrogen limited; densely planted and nitrogen limited; sparsely planted but adequately fertilized; and densely planted and adequately fertilized. The FAO-56 reference-crop method was used to calculate Kcb and ETa in Eq. 4 on daily time steps to predict soil moisture depletion and to schedule irrigations. For comparison, Kcb was replaced by an NDVI term derived from lysimeter studies in a companion study (Hunsaker et al. 2007). In these studies NDVI was measured with a hand-held radiometer two to four times per week in all treatment plots. Actual soil moisture depletion was measured with a neutron hydroprobe in probe ports installed in plots. The NDVI method gave more accurate predictions of actual irrigation demands than the FAO-56 method under all treatment conditions (P \ 0.05) (Hunsaker et al. 2007). For dense stands of wheat receiving adequate fertilization, the FAO-56 method tended to underestimate irrigation requirements by about 10%, whereas for the sparsely planted, nitrogen-limited plots, the FAO-56 method overestimated irrigation requirements by up to 52%. The NDVI method had a root mean square error of about 15% of measured water use with no bias towards under- or over-estimation across treatment. Over both years and all treatments, water use efficiency based on grain yield and water applications was 10% higher for the NDVI method than for the FAO-56 method (P \ 0.05), with a bigger difference for sparsely planted, nitrogen-limited crops. Hence, under actual field conditions, in which crops are frequently growing under suboptimal conditions, use of NDVI measurements as a supplement to static crop coefficients can result in significantly improved irrigation efficiency. In practice, the NDVI measurements needed for this method could be determined by aerial surveys covering large areas of fields, or by frequent-return satellite sensor systems, rather than by ground radiometric measurements. Murray et al. (2009) used MODIS imagery to extend the approach to crops grown in irrigation districts along the Lower Colorado River in the U.S., while Mallick et al. (2007) used a similar approach to estimate ET over agroecosystems in India. Gonzalez-Dugo et al. (2009) compared two TIR-SEB methods with the FAO-56 NDVI method described above to estimate ET over corn and soybean fields in central Iowa, using Landsat imagery over 12 fields equipped with eddy covariance moisture flux towers. Root mean square errors were 0.4–0.6 mm d-1 for the SEB methods and 0.4 mm d-1 for the NDVI method (about 10% of the mean value). Thus, the level of accuracy for SEB and VI methods was the same but the sources of error differed. Some methods combine both VI and LST methods to estimate crop cover and ET (e.g. French et al. 2010). The so-called ‘‘dual source’’ models for agricultural ET use VIs to partition the landscape into bare soil and vegetation, then they estimate transpiration from

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the vegetated fraction based on ETo, and evaporation from the bare soil fraction based on LST (reviewed in Kustas and Anderson 2009). The initial estimate of plant transpiration is adjusted downward, if necessary, based on the surface energy budget in Eq. 1. These combined approaches have potential advantages over other methods in being able to detect insipient plant stress through the LST component, yet inheriting the accuracy of the transpiration/VI relationship.

4 VI Methods to Estimate ET in Natural Ecosystems 4.1 Overview of Approaches Plants in natural ecosystems can violate some of the assumptions underlying the crop coefficient method of estimating ETa. First, natural ecosystems generally contain mixes of plant species, and these will not necessarily have the same relationship between ETa and VI* as a single crop, yet individual species are difficult to resolve even with high resolution imagery. Second, the crop coefficient approach assumes that the plant is growing under unstressed conditions, and that there is a fixed or at least predictable relationship between ETo and leaf-level transpiration in a stand of plants. Mata-Gonzalez et al. (2005) challenged the application of crop coefficients to natural ecosystems, suggesting that they could over-estimate actual plant water use by 50–100%, especially in arid regions where heat and moisture stress are common. Third, there is no simple way to estimate the amount of direct evaporation that contributes to total ETa. Despite these apparent obstacles, a number of successful VI methods have been developed to estimate ETa in a wide variety of landscape types, including rainforests (Juarez et al. 2008), arctic tundra and boreal forests (Mu et al. 2009 Zhang et al. 2009b), riparian zones (Nagler et al. 2005a, b, 2009a, b; Murray et al. 2009; Scott et al. 2008; Barz et al. 2009), desert phreatophyte communities (Groeneveld et al. 2007), semi-arid grasslands (Alfieri et al. 2009; Nagler et al. 2007) and shrublands (Nagler et al. 2007), sparse desert shrublands (Glenn et al. 2008b), and mixed landscapes at the regional (Juarez et al. 2008; Boegh et al. 2009; Scheffield et al. 2009; Wang et al. 2007; Wang and Liang 2008; Leuning et al. 2008; Li et al. 2009; Zhang et al. 2009a), continental (Cleugh et al. 2007; Guerschman et al. 2009; Yang et al. 2006) and global (Mu et al. 2007; Fisher et al. 2008) scales of measurement. Examples are presented in Table 1. Typically, ground measurements of ET from flux towers set in natural ecosystems are used to develop best-fit equations between ET, satellite-derived VIs, ancillary remote sensing data, and ground meteorological data. The studies in Table 1 each used from 4 to 25 tower sites distributed over different ecological units within the biome of interest, and correlated tower data with remotely-sensed VIs over a period of several years. Various statistical tests are used to evaluate the models, but nearly all report the coefficient of determination (r2), which denotes the fraction of measured ET that can be explained by the model. For the studies in Table 1, r2 values ranged from 0.45 to 0.95. Root mean square errors (RMSE) of LE were less than 50 W m-2 and ranged from 10 to 25% of mean ET values over the studies, also within the range of error associated with SEB methods or with measurement errors from the flux tower sites (Courault et al. 2005; Jiang et al. 2004). Two similarities stand out among the studies in Table 1. First, all but one used MODIS as the satellite sensor system of choice. The Terra satellite provides near-daily coverage of the Earth, and MODIS pixels have a resolution of 250 m in the Red and NIR and 500 m in the Blue, an improvement over the AVHRR system with 1 km resolution

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Table 1 Examples of vegetation index methods for ET and coefficients of determination with moisture flux tower data Location

Plant communities

Explanatory variables

r2

References

Middle Rio Grande, USA

Arid-zone riparian trees

MODIS EVI, Ta

0.82

Nagler et al. (2005a)

Walnut Gulch, AZ, USA

Desert shrubs and grasses

MODIS EVI, precipitation

0.74

Nagler et al. (2007)

San Pedro River, Riparian trees, shrubs, USA grasses

MODIS EVI, LST

0.93

Scott et al. (2008)

Lower Colorado River, USA

Riparian shrubs and trees

MODIS EVI, ETo

0.80

Nagler et al. (2009a, b)

Three Western USA rivers

Riparian trees, shrubs, grasses

MODIS EVI, Ta

0.76

Nagler et al. (2005b)

Southwestern USA

Phreatophyte shrub communities

Landsat NDVI, ETo

0.96

Groeneveld et al. (2007)

Southern Great Plains, USA

Native prairie, rangeland, pastures

MODIS EVI, Rn, soil moisture

0.82

Wang and Liang (2008)

MODIS EVI, Rn

0.72–0.86 Juarez et al. (2008)

Amazonia, Brazil Rain forest trees Murray-Darling Basin, Australia

Evergreen forests, tropical MODIS LAI, proxies for savannas variables in Eq. 6

Pan-Arctic North Boreal forests, grasslands, MODIS LAI, NDVI, ground America tundra meteorological data Pan-Arctic Basin Boreal forests, tundra, peatlands

0.66–0.90 Zhang et al. (2009a, b) 0.45–0.89 Mu et al. (2009)

AVHRR NDVI, MODIS Land 0.91 Cover, solar radiation, albedo

Australia

Evergreen forests, tropical MODIS LAI, ground savannas meteorological data

Australia

Forests, savannas, grasslands, floodplain, lake

Zhang et al. (2009a, b)

0.74

Cleugh et al. (2007)

MODIS EVI, Global Vegetation 0.84 Moisture Index, ETo

Guerschman et al. (2009)

Continental-scale Forests, grasslands, North America shrublands, croplands

MODIS EVI, LST, solar radiation, land cover class

0.75

Yang et al. (2006)

Continental US

MODIS EVI, LST, MODIS Land Cover, SWR

0.75

Yang et al. (2006)

MODIS LAI, proxies for variables in Eq. 6

0.80

Leuning et al. (2008)

0.90

Fisher et al. (2008)

Shrublands, grasslands, forests, crops

Global at Fluxnet Crops, wetlands, forests, Sites grasslands, savannas

MODIS and AVHRR NDVI, Global at Fluxnet Grasslands, crops, Sites deciduous and evergreen SAVI and EVI, Rn, Tmax, forests VPD Entries are arranged by spatial scale of coverage, from local to global

(Huete et al. 2002). Furthermore, data are available as georeferenced and atmospherically corrected VI or LAI products, in which composites of cloud-free images are prepared for 8-day or 16-day intervals in near real time. Thus MODIS lends itself to time-series analyses of ET and other physiological processes. Second, EVI was overwhelming preferred over NDVI as the VI of choice. Several studies (e.g., Nagler et al. 2005a, 2007; Wang et al. 2007) showed that MODIS EVI was significantly better correlated with ground-based ET measurements than MODIS NDVI across a variety of land cover types,

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Fig. 2 Comparison of correlation coefficients between ET measured at flux towers and Normalized Difference Vegetation Index versus Enhanced Vegetation Index values for MODIS pixels encompassing the tower sites (from Nagler et al. 2005a, b, 2007)

541

EVI:ET Correlation Coefficient

Surv Geophys (2010) 31:531–555 1.0

1:1

0.9

0.8 Mesquite Giant Sacaton Saltcedar Cottonwood Arrowweed Desert Grassland Desert Shrubland

0.7

0.6

0.5 0.5

0.6

0.7

0.8

0.9

1.0

NDVI:ET Corrrelation

as predicted also by Choudhury et al. (1994) in their comparison of NDVI versus SAVI. Nagler et al. (2005a, b, 2007) reported correlation coefficients of 0.83 for EVI but only 0.72 for NDVI on ET measured at 11 flux tower sites in riparian and upland sites in the southwestern US (Fig. 2). 4.2 Requirements for Ancillary Data VI methods work for two basic reasons. First, transpiration generally dominates over direct evaporation in determining ET in most landscape types. Even in sparse deserts, rainfall tends to be efficiently captured by vegetation (Glenn et al. 2008b), and across agricultural and natural ecosystem, transpiration usually accounts for 70% to [90% of ET (Huxman et al. 2004; Williams et al. 2004). Second, plants tend to be conservative in their production of leaves. The resource optimization theory (Field 1991; Field et al. 1995; see also Albrizio and Steduto 2003, for agricultural crops) states that plants adjust their foliage density to match the capacity of the environment to support photosynthesis, which can be limited by nutrients, water or other factors. Hence, a measure of green foliage density by remote sensing is a good first step in estimating ET over a variety of landscape types. However, VIs by themselves are not always sufficient for estimating ET (Glenn et al. 2007). VI methods require estimates of atmospheric water demand and the energy available to evaporate water, which can be provided by remote sensing and meteorological data; estimates of stomatal or canopy conductance per unit leaf area; and an estimate of direct evaporation of water from soil or the canopy following precipitation events. VI methods vary widely in complexity and approach in estimating these additional variables, depending on the applications for which they were developed. Applications of VI methods to specific biomes, ranging from the simple to complex, are illustrated in the following sections. 4.3 Estimating ET by Arid Zone Phreatophyte Communities Phreatophytes are shrubs or trees rooted into underground water supplies. They are the dominant vegetation type over millions of hectares of western US internal drainage basins, where mountain recharge creates valley aquifers within rooting distance of these specialized plants, which can extract water from 8–18 m soil depth (Nichols 1993;

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Jordan et al. 2008). Phreatophytes are also the dominant vegetation type along western US rivers, where the aquifer is typically much closer to the surface (1–5 m depth) (Horton et al. 2001). Determining phreatophyte water use is critical in constructing regional water budgets, especially when there is competition between humans and natural ecosystems for limited groundwater supplies. VI methods lend themselves to determining ET in these ecosystems (Groeneveld and Baugh 2007; Groeneveld et al. 2007). Atmospheric water demand can be determined from wide-area meteorological data. Canopy conductance is often not affected by moisture stress since the plants have access to a constant source of water in the aquifer. Furthermore, ET is overwhelmingly dominated by plant transpiration in these systems since precipitation is low and surface soils are normally dry. Groeneveld and Baugh (2007) developed a simple method for estimating annual ET of desert and riparian phreatophytes based on single, mid-summer NDVI images from Landsat 5. They atmospherically corrected the images using the dark-body subtraction method, in which a body of water (e.g., farm ponds) with assumed zero reflectance in the NIR, was used to calibrate Red and NIR reflectance values across whole scenes. They then stretched NDVI between bare soil and maximum NDVI values, again using pixels within each scene as reference points. NDVImax was based on NDVI of alfalfa fields, whereas NDVImin was based on projecting the linear portion of pixel count versus NDVI histogram to zero. They then determined ETo using data from micrometeorological stations equipped to solve Eq. 6, and calculated ETa by Eq. 9, using their scaled NDVI (NDVI*) and a value of 1 for g. They tested the method against 24 summer Landsat images collected over 15 sites for which flux tower data was available (Groeneveld et al. 2007). Habitat types included desert and riparian phreatophyte communities across the southwestern US, with ET rates ranging from 50–1,400 mm year-1. A 3 9 3 pixel array (ca. 900 m2) around each tower site was selected for comparison. Modeled ET rates were similar to measured rates across the range of ET rates and plant types, with an r2 of 0.94 (Fig. 3) and a RMSE of about 20% of the mean ET value. This method was subsequently used to conduct a cost-benefit analysis of saltcedar (Tamarix ramosissima) removal along the Pecos River in Texas (Barz et al. 2009). Saltcedar ET rates were much lower than had been projected from earlier, indirect methods for ET estimation, and the prospects for water salvage were judged to be low and uneconomical compared to the cost of saltcedar removal. Nagler et al. (2005a, b) developed a time-series method for riparian phreatophyte ET in the southwestern US, using MODIS EVI and meteorological data. They used multi-year moisture flux tower data from nine towers on three western US river to develop a MODIS ET algorithm that could be used across the major riparian species, including mesquites (Prosopis spp.), giant sacaton grass (Sporobulus wrightii), saltcedar, cottonwood (Populus deltoides)., and arrowweed (Pluchea sericeae). MODIS EVI was significantly better correlated with ET than with NDVI, and maximum daily air temperature (Tmax) was the only environmental variable that improved the ET prediction based on multiple regression analyses. The final algorithm used a scaled EVI* from bare soil (EVI = 0.091) to full vegetation (0.542), in the form of an exponential equation based on the formula for the extinction of light in a plant canopy. The Tmax term was based on a sigmoidal relationship between temperature and plant transpiration, in which there was a lower limit of about 20°C, below which transpiration was zero, and an upper limit at about 32°C, where transpiration did not continue to increase. The algorithm also had a constant term (1.07 mm d-1), representing direct evaporation, because the tower ET rates did not go to zero even in winter when plants were dormant. The r2 for the ET algorithm was 0.76

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Fig. 3 Regression of actual annnual evapotranspiration (ETa) and NDVI scaled between 0 ETa and maximum ETa based on ETo calculated from the Penman–Monteith equation, based on measurements of ETa and micrometeorological data from moisture flux tower sites in native phreatophyte communities in the western US (from Groeneveld et al. 2007)

and the RMSE was 25% of the mean ET value across measurement sites. The equation of best fit was:  

ð11Þ ETa mm d1 ¼ 11:5 1  e1:63EVI ð:832= 1 þ eðT max 27:9Þ=2:57 þ 1:07 Scott et al. (2008) subsequently simplified the algorithm, and showed that MODIS LST could substitute for Tmax in the algorithm, making the method independent of ground meteorological data. The remotely sensed ET estimates agreed well with catchment water balance estimates. These algorithms were used to compare ET rates on western rivers that contained different mixes of plants. A specific goal was to determine the water use of saltcedar compared to native plants, as this introduced species has been targeted for removal as a high water-use species. The surveys showed that ET on three rivers that differed in amount of saltcedar, from\5 to[80%, all had similar, moderate, rates of water use, corresponding to less than 50% of ETo (Nagler et al. 2005b). More recently, Nagler et al. (2009a, b) developed an algorithm for riparian and agricultural ET based on MODIS EVI and ETo determined from meteorological data, similar to the approach of Groeneveld et al. (2007), and to methods used for crop plants. They correlated EVI* with ET data measured in alfalfa, saltcedar, arrowweed and cottonwood plots on the Lower Colorado River. ET was expressed as a fraction of ETo (EToF), with ETo calculated either by the Penman–Montheith equation (ETo-PM), or the much simpler Blaney–Criddle method (ETo-BC), which requires only mean monthly temperature and latitude data. ETo-BC provided a better fit between EToF and EVI* than ETo-PM (Fig. 2) and the equation of best fit was:
ð12Þ ETa mm d1 ¼ 1:22 EToBC ðEVIÞ The RMSE was about 20% of the mean ET value. Use of ETo-BC greatly increases the degrees of freedom in projecting ETa by remote sensing; for example, Arizona has over

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500 cooperative reporting stations where temperature and precipitation are measured, but only 25 AZMET stations where ETo-PM is calculated. Equation 12 is very similar to the algorithm used by Groeneveld for phreatophyte ET based on Eq. 9. The coefficient 1.22 is required because ETo-BC is about 10% lower than ETo-PM along the Lower Colorado River, and because EVI* was based on a maximum value of 0.542 determined in dense riparian vegetation, which does not necessarily exactly match the EVI of the hypothetical reference crop in Equation (8). This method was used to estimate both riparian and agricultural ET rates along the Lower Colorado River from Lake Mean to the US/Mexico border. The mean EToF (ET/ETo) for agricultural crops was 0.73 by MODIS estimates, compared to a value of 0.63 set by expert opinion. On the other hand, riparian EToF was only 0.4, compared to a value of 0.9 set by expert opinion. This study corroborates other recent studies that saltcedar-dominated riparian systems have low to moderate ET rates, contrary to earlier expectations. Riparian ET estimated by Eq. 12 was about 20% lower than estimated by Eq. 11. Most of the ground data used for Eq. 12 was derived from sap flux sensors, which measure the flow of water through plant stems (transpiration), and do not include direct evaporation as did the flux tower measurements used to derive Eq. 11. Hence, the results illustrate that the accuracy of VI methods is very much determined by the accuracy of the ground ET methods by which they are calibrated. The sap flux data (Nagler et al. 2009a, b) showed that saltcedar plants can be under considerable stress, as shown by midday depression of transpiration and stomatal conductance at most of the sap flux sites. However, saltcedar also had nocturnal water loss through salt glands and stomata, which accounted for as much as 20% of total water loss from canopies. Therefore, mean daily water loss per unit leaf area was similar to crops and other riparian plants, with a coefficient of variation of about 20% around the mean. 4.4 ET Over Mixed Ecosystems Several research groups have attempted to develop more general VI methods that could be applied across different biomes to derive continental or global-scale estimates of ET to be used in global climate change studies (Table 1). These groups are attempting to develop methods to scale point measurements of carbon, moisture and energy fluxes measured at FLUXNET, AmeriFlux, or other eddy covariance or Bowen ratio tower sites to larger landscape units (Baldocchi et al. 2001). The ultimate goal is to provide long-term measurements of ecosystem net primary productivity, carbon exchange and ET, to be used in regional and global models responsive to climate forcing and land use change scenarios. A common feature of these efforts is that they use MODIS time series data. Some studies have inter-calibrated AVHRR and MODIS data to create time-series records from the 1980s to the present (e.g., Zhang et al. 2009b). They typically calculate ET in monthly time steps, consistent with the 8-day or 16-day MODIS compositing periods, and with the modulated response of foliage density to changes in environmental variables. Yang et al. (2006) used a statistical approach to estimating ET over the continental US based on ET estimates from 25 AmeriFlux sites in grasslands, shrublands, croplands and forests. They divided their data into training and testing (validation) sets. They used MODIS EVI, LST and Land Cover (LC) products as remote sensing inputs, in addition to ground measurements of incident shortwave radiation (SWR). ET values and explanatory variables were entered into a machine learning program in which non-linear regression analyses produced an algorithm of best fit. EVI was the most important explanatory

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variable, followed by SWR, LST and LC. The best-fit algorithm was applied to testing data withheld from the training set, and predicted tower ET with an r2 of 0.75 and a RMSE equal to 23% of the mean ET. They then applied their model to the entire continental US, and it successfully captured phenological and elevation trends expected across continental biomes. A disadvantage of this approach is that the data combinations incorporated into the machine learning program were not directly comprehensible by the programmer; this is a ‘‘black box’’ approach to estimating ET. Other groups have developed more mechanistic VI-ET models, constrained by the variables in Eqs. 1 and 6. One approach is to use ground and remote sensing inputs to estimate the key variables in the Penman–Monteith equation. Cleugh et al. (2007) developed an ET model for two Australian ecosystems using the MODIS LAI product as the main remotely sensed variable, in a simple model for surface conductance (GS): GS ¼ cL ðLAIÞ þ GS;min

ð13Þ

where cL is the mean surface conductance per unit leaf area (determined from flux tower data and treated as a constant); and GS,min is soil conductance to account for bare soil evaporation. GS can be converted to a resistance term (G-1 S ), and used as rs in Eq. 6. The other terms in Eq. 6 can be approximated from meteorological and remote sensing data to solve for ETa. The model had an r2 of 0.74 when compared with flux tower data, whereas an SEB model based on Eq. 1 and MODIS LST had an r2 of only 0.41 and was judged to be unsuccessful. Mu et al. (2007) improved this model at 19 Ameriflux sites by adding scaling factors between 0 and 1 to account for the physiological response of stomata to changes in VPD and Ta (plants partially close stomata at high VPD and Ta). They introduced a separate term to estimate direct evaporation from bare soil based on the relative humidity of the air over the soil surface. This model successfully predicted ET across the continental US when compared to watershed models. Leuning et al. (2008) developed a more generalized form of the model based on data from 15 Fluxnet sites in a variety of vegetation communities. MODIS LAI was the main remote sensing parameter. Meteorological and biophysical data from each flux tower site were used to parameterize six variables that represent canopy physiological and soil evaporation processes incorporated into Eq. 6. These included maximal stomatal conductance; values of Rn and VPD when stomatal conductance is half maximal; extinction coefficients for light and available energy; and the ratio of soil evaporation to the equilibrium rate for wet soil, corresponding to the energy received at the soil surface. These additional parameters were optimized for each biome type, which were identified by the MODIS land cover product. The model had an r2 of 0.80 and performed better than the simpler model developed by Cleugh et al. (2007). A disadvantage of Eq. 6 as a model for ETa is that it has several terms that are difficult to estimate over mixed landscapes or with limited data. Other VI-ET models have been based on the Priestley–Taylor equation for maximum latent heat flux (LEmax) over a uniformly moist surface (Priestley and Taylor 1972): LEmax ¼ aðRn  GÞ  D=ðD þ cÞ

ð14Þ

Equation (14) is based on the assumption that, under equilibrium conditions, maximum LE over an extensive wet surface should be limited by the amount of energy available to evaporate water (Rn-G); a is an empirical term, usually set at 1.26, to accommodate observational data over a variety of well-watered surfaces. ETo in mm d-1 can then be calculated from LEmax using the latent heat of evaporation of water. The Priestley–Taylor

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potential ET (ETo-PT) lends itself to remote sensing studies because G can be assumed to be zero over daily time steps, hence ETo-PT can be determined solely from Rn, which can be accurately determined from ground or remote sensing data. Guerschman et al. (2009) used bidirectional-distribution-function (BRDF) corrected MODIS products to obtain reflectance values in each band that were independent of view angle, then calculated monthly values of the MODIS-derived Global Vegetation Moisture Index (GVMI) and EVI. They combined the remote sensing data with Eq. 14 to determine ETa over Australia. The GVMI estimates surface water content (in plants and soil) by the ratio of reflectance in the NIR to the shortwave IR (SWIR, 1640 nm), based on the strong reflectance in the NIR compared to the SWIR. EVI was used as a measure of LAI, and as an initial assumption, maximum plant transpiration was assumed to be equal to ETo-PT at EVImax and to equal zero at EVImin, as in other methods. ETa was scaled between zero and ETo-PT using a sigmoidal rather than a linear equation. An innovation of this method was the use of a Residual Moisture Index (RMI) to delineate open water areas and wet soil. EVI and GVMI are expected to be highly correlated if surface moisture is due to vegetation; but they are uncorrelated if surface water is due to wet soil or open water. By plotting the residuals of the EVI:GVMI regressions, vegetated surfaces could be distinguished from unvegetated wet surfaces, and the evaporation from these areas could be calculated separately. This model also incorporated a term for direct evaporation of water from canopies following rain events, based on precipitation data. The model was then calibrated with ETa and other data from seven sites representing grasslands, forests, a lake and a wetland ecosystem. The final model had an r2 of 0.84 and an RMSE of 23% of the mean measured at flux tower sites, and was able to project ET accurately over the entire content, as compared to water catchment observations. Up to now, the ET models reviewed have all required at least some ground data, and were calibrated by reference to flux tower ET data. Fisher et al. (2008) developed a VI-based ET model that did not require parameterization of inputs; did not require intensive field measurements; yet incorporated mechanistic realism. Their goal was to develop a global model for ET, and they recognized that ground data is sparse over much of the globe. They used ETo-PT to constrain maximum ETa based on MODIS-derived values for Rn (assuming G was zero on a daily time step). They then adjusted ETa downward based on plant physiological and soil moisture limitations. ETa was divided into three components which were estimated separately: plant transpiration; evaporation from soil; and evaporation of water intercepted by canopies during a rain. Four physiological limitations to plant transpiration were calculated: LAI (estimated with NDVI); fraction of the green canopy cover that is actively transpiration (estimated with NDVI and SAVI); plant temperature (from modeling and ground measurements of Tmax); and moisture stress (considered a minor constraint at most sites, and estimated by the decrease in green cover). Soil evaporation was estimated from midday values of relative humidity and VPD over bare soil, by assuming that near-surface atmospheric moisture content reflected the evaporation rate from the soil; and evaporation of intercepted rainfall was modeled based on potential ET times the fraction of time the leaves were wet (when relative humidity = 100%). They tested their model using AVHRR imagery and 2 years of data from 16 Fluxnet stations in grasslands, croplands, wetlands, savannas and deciduous and evergreen broadleaf and conifer forests, and obtained an r2 of 0.90 and a RMSE of 28% of mean ETa (Fig. 4). They applied their model at the global scale and it successfully reproduced regional trends (Fig. 5), as well as disturbances in the hydrological cycle due to El Nino events and the eruption of Mount Pinatubo.

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Fig. 4 Modeled latent heat of evaporation (LE) versus measured LE at 16 Fluxnet moisture flux tower sites around the world, based on 2 years of data and using MODIS and AVHRR and ISLCP-II data (from Fisher et al. 2008)

The different regional to global VI models have been used in a variety of practical applications including improving rainfall-runoff models in South East Australia (Zhang et al. 2009a, b), detecting northern ET trends from 1983 to 2005; and assessing land surface evaporation in the Pan-Arctic domain (Mu et al. 2009). Combined with Fluxnet and other ground measurements, these new ET methods are becoming part of the routine Earthmonitoring tools on which climate change modeling depends.

5 Limitations of VI Methods Perhaps the most serious limitation to both VI and SEB remote sensing methods for ET is the accuracy of the ground data by which they are calibrated or validated. Eddy covariance flux towers currently provide the best estimates of ET over footprint areas that overlap satellite imagery. Yet they have an error or uncertainty of about 10–30% based on comparison of multiple towers at the same site, or by comparison with independent measurements of ET by other methods such as lysimeters or sap flux sensors (reviewed in Glenn et al. 2007). Eddy covariance towers frequently have a ‘‘closure error’’ of about 10–30% when tower-based LE values are applied in Eq. 1 (Mahrt 1998). ET values are typically corrected for closure error (e.g., Chavez et al. 2009), but the cause of lack of closure, and how to best correct for it, are still uncertain (Shuttleworth 2007). VI methods for ET cannot detect early signs of plant moisture stress, so they are not useful for real-time irrigation scheduling (Kustas and Anderson 2009). By the time moisture stress is manifested as a reduction in LAI that can be detected by VIs, the crop will likely have suffered a yield reduction. However, on monthly time steps, the NDVI-Kc methods developed by Hunsaker et al. (2005a, b) and others (Neale et al. 2005) are useful in closely matching crop water demand to crop growth and development, with a potential for water savings over the life of the crop. The extension of that method to entire irrigation districts on the Lower Colorado River using MODIS shows the potential for replacing fixed Kc values with near-real-time measurements based on the actual state of the crops,

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Fig. 5 Global distribution of ET for 1993 by the model of Fisher et al. (2008)

potentially improving irrigation district water budget estimates (Murray et al. 2009). However, presently there are not enough ground measurements of crop ET at spatial scales relevant to satellite imagery to calibrate the methods. In natural ecosystems, VI methods are more useful as a passive monitoring tool for ecosystem water use than as an active, rapid-response tool to mitigate incipient moisture or

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other stresses. Nagler et al. (2009a, b) showed that the phreatophyte shrub, saltcedar, grows under considerable stress that varies among sites, due to soil and salinity constraints. Therefore, the assumption that phreatophytes grow under unstressed conditions because they have constant access to water was not supported. However, with enough ground data from representative stands, a usable relationship between MODIS EVI, ETo, and ET was developed for this river system. We caution that extending any of these methods to other biomes or applications beyond those for which they were calibrated or validated would require recalibrating the constants and doing enough ground studies to understand the ecophysiological limits on the plants of interest for each application. Like SEB methods, the more complex VI methods for mixed ecosystems are subject to the problem of equifinality, in which different models with different assumptions and levels of complexity produce similar results (Beven 2006). This is a problem in many Earth science disciplines. It is particularly a problem in remote sensing studies, because satellites typically provide data in just a few spectral bands. For example, some of the studies cited above require separate estimates of LAI, fractional vegetation cover, stomatal conductance and other biophysical parameters. Yet they are typically estimated by VI products that are themselves highly cross-correlated such as SAVI, NDVI, EVI, or the MODIS LAI and APAR products, most of which are simply combinations of Red and NIR reflectance values. Furthermore, the ground estimates of ET on which they are calibrated or validated are subject to errors of up to 20–30% (Jiang et al. 2004). Therefore, the mechanistic reality of the models is difficult to evaluate. The methods in Table 1 range from the very simple (e.g. Groeneveld and Baugh 2007) to the more complex (e.g., Fisher et al. 2008), without a concomitant increase in accuracy. One reason that simple models work as well as multifactor models is that plant productivity (and transpiration) tend to be limited by a single factor at a given time and place (Liebig’s law of the minimum) (Paris 1992), although at the community level co-limiting factor might operate (Danger et al. 2008).

6 Combining Ground and Remote Sensing Methods A way out of the equifinality dilemma is to combine ground and remote sensing studies with modeling to obtain a more complete understanding of ecosystem dynamics than could be gained by any component alone (Running et al. 2004; Pan et al. 2010). This is the stated goal of the Fluxnet, Amerinet and other flux tower networks; MODIS was launched specificially to provide a scaling tool to project tower findings to local, regional and global scales of measurements (Baldocchi et al. 2001). The measure of success of the remote sensing components is not in how faithful they are to mechanistic models, but in how they can enhance our understanding of ecohydrological processes in Earth sciences as part of an ensemble of observational data. A successful recent example of this approach is the discovery of high dry-season ET rates in the Amazon rain forest (Harper et al. 2010). Global Climate Models (GCMs) had predicted a possible conversion of the rainforest to savanna grasslands in the twenty first Century due to a regional drying trend that might be induced by global warming (Cowling et al. 2004). This could theoretically create a positive feedback on global warming due to the release of carbon stored in tree biomass to the atmosphere (Cox et al. 2004). However, flux tower data combined with MODIS EVI monitoring showed that large portions of the Amazon forest actually have maximum ET and foliage density in the dry season (Huete et al. 2006). Ground data showed that trees can extract water from up to 18 m or deep in the soil profile, whereas the models used a 2 m soil moisture storage depth. Contrary to the

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models, observation data showed that trees were radiation-limited during the rainy season due to cloud cover, and were simulated by greater Rn during the dry seasons, using water stored in the deep soil profiles. GCMs are currently being adjusted to accommodate the observational findings, with important implications on how to manage the Amazon forests for the future (Malhi et al. 2009). A similar combination of approaches has been used to improve our understanding of riparian ET, particularly the role of saltcedar in western US riparian water budgets. Early, indirect methods of estimating ET suggested that it could use 3–4 m year-1, and that considerable water could be salvaged by eliminating it from western streams (reviewed in Di Tomaso 1998; Owens and Moore 2007). A combination of flux tower, sap flux, and remote sensing studies has now led to a downward revision of saltcedar water use (reviewed in Nagler et al. 2010), increasing the number of degrees of freedom that water managers have in accommodating both human and environmental water demands.

7 Future Operational and Research Needs In the past 5 years, new VI methods have been developed to estimate ET over a wide variety of natural and agricultural ecosystems. Part of their success can be attributed to the availability of MODIS imagery, which provides near-daily coverage of the globe at optical-band resolutions that at least partly overlap the footprint of ground measurements by which they are validated. However, the Terra satellite is now beyond its projected lifetime, threatening a potential gap in coverage until the replacement National Polarorbiting Operational Environmental Satellite System (NPOESS) with its Visible/Infrared Imager Radiometer Suite (VIIRS) is launched in late 2014 (http://www.ipo.noaa.gov/ index.php#). A NPOESS Preparatory Program (NPP) mission with prototype VIIRS sensor is scheduled for launch in 2012 and will provide a bridge to any gap in coverage. The VIIRS sensor will provide satellite VI (NDVI, EVI) as well as LST products, known as Environmental Data Records (EDRs). If continuity is provided through future satellite launches, inter-calibrated VI values from AVHRR, Terra, Aqua and VIIRS replacement satellites will be able to provide records of global changes in ET and other plant physiological processes starting in 1981. Higher resolution imagery suitable for ET studies will be available from the Landsat Data Continuity Mission scheduled for launch in December, 2012, from the HyspIRI scheduled for 2014–2017 (Hook and Oaida 2010) and from commercial satellite such as Digital Globes WorldView and Quickbird satellites (http://www.digitalglobe.com/index.php/ 82/Content?Collection?Sytems). Hence, the VI methods for ET described in this review will likely be key tools in Earth observing sciences for many years to come. VI methods are ultimately limited by the accuracy of the ground data by which they are calibrated and validated. The primary source of ground data has been flux towers (exceeding 500) now set up in biomes around the world (Baldocchi et al. 2001). Although the towers are gathered into data-sharing networks, they tend to be individually funded through a variety of sources, differing in the period over which funding is committed. The flux towers are essential in testing ecophysiological and meteorolgical constraints on plant transpiration and photosynthesis, and it is probably unrealistic to think that remote sensing data will be able to replace these functions. Hence, expanding the network of flux towers and providing continuity of operation are arguably as important as providing continuity of remote sensing platforms.

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Furthermore, if flux tower and other ground methods for ET can be improved beyond the present error or uncertainty of 10–30%, the remote sensing methods will likely improve in accuracy as well. Under ideal conditions, when ET is measured in precision weighing lysimeters and VIs are measured with hand-held radiometers not subject to atmospheric effects, measured and modeled ET values are within 5% of each other (e.g., Hunsaker et al. 2005a, b), showing the tight relationship between leaf area, VIs, and transpiration. Flux tower results can be refined by using alternative ET methods such as sap flux sensors for validation (reviewed in Glenn et al. 2007). It is important to note that while the accuracy (deviation from the true value) of VI methods is limited by the ground methods, the precision (ability to detect differences between measurements) is much greater due to the ability of VIs to quantify green vegetation and therefore processes that depend on foliage density (Bannari et al. 1995). Hence, rather subtle changes in ET can be detected in response to forcing events (e.g., Dennison et al. 2009). Additionally, TIR methods can be incorporated to detect early effects of stress that have not yet resulted in decreased LAI, and they can be used to constrain ET estimates by the SEB equation (Eq. 1) (Kustas and Anderson 2009). Hence, remote sensing estimates of ET are likely to improve in the future due to improvements in satellite and ground data sources, and through integration of TIR and VI methods to provide validated ET estimates over an expanded range of temporal and spatial scales of resolution.

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