Comparison of three remote sensing based models to estimate evapotranspiration in an oasis-desert region

Agricultural Water Management 165 (2016) 153–162

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Comparison of three remote sensing based models to estimate evapotranspiration in an oasis-desert region Jinjiao Lian a,b , Mingbin Huang b,∗ a

College of Resources and Environment, Northwest A&F University, Yangling, 712100, China State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Soil and Water Conservation, Northwest A&F University, Yangling, 712100, China b

a r t i c l e

i n f o

Article history: Received 27 July 2015 Received in revised form 25 November 2015 Accepted 1 December 2015 Available online 8 December 2015 Keywords: METRIC The Ts -VI triangle model SSEB The contextual method

a b s t r a c t Regional evapotranspiration (ET) estimation is crucial for regional water resources management and allocation. This paper evaluated the performance of three contextual remote sensing based models for ET estimation (METRIC—Mapping Evapotranspiration at High Resolution with Internalized Calibration; the Ts -VI triangle model; and SSEB-Simplified Surface Energy Balance) in an oasis-desert region during a growing season under advective environmental conditions. The performance of the three models was first assessed using surface fluxes observed at five eddy covariance (EC) flux towers installed in different land-cover types. Comparisons among model outputs were then conducted on a pixel-by-pixel basis for three main land-cover types (farmland, transition zone and desert). For METRIC and SSEB, good correlations were obtained between the modeled versus measured instantaneous latent heat flux (ET), with both R2 values above 0.90. Outliers occurred when available energy was overestimated for the Ts -VI triangle model. Pixel-wise comparisons showed the greatest consistency between the Ts -VI triangle model and METRIC outputs in farmland with an R2 of 0.98 and an RMSE of 13.69 W m−2 . Overall, METRIC outperformed both the Ts -VI triangle and SSEB models; the Ts -VI triangle model tended to overestimate and the SSEB to underestimate at higher values of ET. ET estimations by SSEB and the Ts -VI triangle model are more sensitive to the estimated surface temperature and available energy than those from METRIC. Two daily ET extrapolation methods were evaluated with the EC measured daily ET . The results indicated that the constant reference ET fraction (ETr F) method could be used over well-watered areas due to the regional advection effect; the constant evaporative fraction (EF) method tended to give better outputs for other areas. Reasonable estimates of ET can be achieved by carefully selecting extreme pixels or edges, and validation is required when applying remote sensing based models, especially the contextual methods. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Evapotranspiration (ET) is an important part of both the water and energy cycle. The spatio-temporal variation of ET has been widely used to inform regional water resources management and allocation, including irrigation scheduling, drought monitoring and forecasting. Remote sensing techniques, characterized by high temporal, spatial, and spectral resolution, have been a viable and economical way to map ET in heterogeneous regions. Many models with different degrees of complexity have been developed in recent

∗ Corresponding author. Fax: +86 29 87012210. E-mail address: [email protected] (M. Huang). http://dx.doi.org/10.1016/j.agwat.2015.12.001 0378-3774/© 2015 Elsevier B.V. All rights reserved.

decades to obtain trends in spatial and temporal variability of ET (Bastiaanssen et al., 1998; Jiang and Islam, 1999; Norman et al., 1995; Su, 2001), which differ with respect to landscape type and spatial extent of model application, type of remote sensing data, and required ancillary meteorological and land-cover data (Kalma et al., 2008). Chirouze et al. (2014) divided remote sensing based ET estimation models into two groups: single-pixel and contextual methods. Single-pixel methods calculate sensitive heat flux (H) and latent heat flux (ET) by solving the surface energy budget for each pixel independently from others; this requires ground-based measurements of vegetation height, surface wind speed, and air temperature (Kustas and Norman, 1999). Representative models that use this method are the SEBS (Surface Energy Balance System) and TSEB (Two-Source Energy Balance) models. Due to the

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limited availability of ground-based characteristics for heterogeneous regions, this type of model is rarely used for ET estimation over large areas for operational applications (Jiang and Islam, 2003). In the contextual method, the pixel-wise H and ET are constrained and scaled by the so-called hot and cold extreme pixels selected within a study area, without the explicit and robust parameterization of aerodynamic resistance (Tang et al., 2011). Wang et al. (2007) pointed out that ET was highly related to surface net radiation, temperature, and vegetation index. Surface parameters, including the surface temperature (Ts ), the normalized difference vegetation index (NDVI) or fractional vegetation cover (fc ), and the surface albedo (˛), are commonly used to form the two-dimensional scatterplot envelope to scale the H or ET. The SEBAL (Surface Energy Balance Algorithm for Land) model and a modified version thereof, METRIC (Mapping Evapotranspiration at High Resolution with Internalized Calibration), employ the contextual method. The slope of the Ts versus ˛ relationship is related to the area-effective momentum flux calculation (Bastiaanssen et al., 1998), and the near-surface temperature gradient (dT) of the hot and cold extreme pixels is used to anchor the linear relationship between dT and Ts . The Ts -VI triangle model estimates ET based on an extension of the Priestley–Taylor equation using the Ts versus NDVI/fc triangle spatial variation (Jiang and Islam, 2001). The evaporative fraction (the ratio of ET to surface available energy, EF) can be obtained for each pixel by interpolating the ϕ parameter (introduced in Section 2.1.2) of the hot and cold edge, and ET can be derived by multiplying the available energy and EF. The SSEB (Simplified Surface Energy Balance) model estimates ET values using only Ts and the maximum ET for the region (Senay et al., 2007). Ts is used as a scalar to indicate the water availability of the pixel by assuming that the hot extreme pixel is located in a dry, bare area with no ET and the cold extreme pixel is located in a well-watered area with the maximum ET. Although these models were developed based on different theories and have different degrees of complexity, reasonable ET values can be generated by all models under certain conditions (Allen et al., 2007a; Khan et al., 2010; Kimura et al., 2007; Li and Zhao, 2010; Liu et al., 2010b; Tang et al., 2010; Tasumi and Kimura, 2013). The Ts VI triangle and SSEB models are comparatively simpler than the METRIC model due to fewer input items. Senay et al. (2011) compared the derived ET fractions of SSEB and METRIC using seven Landsat images acquired for south central Idaho during a growing season. The results exhibited good performance in less topographically complex areas. Several studies have compared outputs from the Ts -VI triangle model with those from the SEBAL, METRIC, SEBS, and TSEB models (Choi et al., 2009; Long and Singh, 2013; Tang et al., 2011). However, all of these studies were conducted in irrigated agricultural areas in sub-humid climates. The comparison of contextual models in an oasis-desert region with multiple landcover types has never been performed, and few studies account for the temporal representativeness of these models (Chirouze et al., 2014). The objective of this paper was to test the performance of three contextual remote sensing based models (METRIC, the Ts -VI triangle model, and SSEB) for ET estimation during the growing season in an oasis-desert region with advective environmental conditions. The performance of these three models was first assessed using ET values observed at five eddy covariance (EC) flux towers installed in different land-cover types. Comparisons among the model outputs were then conducted on a pixel-by-pixel basis for three main landcover types (farmland, desert, and the transition zone in between). As the daily and monthly ET values are more frequently applied in practical water resources management, two extrapolation methods to derive daily ET were evaluated using the daily EC measurements at the five flux towers on satellite overpass dates.

2. Materials and methods 2.1. Model description 2.1.1. METRIC model The METRIC model (Allen et al., 2007b) computes ET as the residual of the surface energy balance: Rn = G + ␭ET + H

(1)

where Rn is the net radiation flux (W m−2 ); G is the soil heat flux (W m−2 ); H is the sensible heat flux (W m−2 ); and ET is the latent heat flux (W m−2 ). The Rn is given by Rn = (1 − ˛) RS,in + ε0 RL,in − ε0 Ts4

(2)

where ˛ is the surface albedo (dimensionless); ε0 is the surface emissivity (dimensionless); RS,in and RL,in are incoming short wave and long wave radiation (W m−2 ), respectively;  is the Stefan–Boltzmann constant (5.67 × 10−8 W m−2 K−4 ); and Ts is the surface temperature (K). The G value is estimated as a fraction of the net radiance using Ts , ˛, and the Normalized Difference Vegetation Index (NDVI): G=

  Ts − 273.16  0.0038˛ + 0.0074˛2 1 − 0.98NDVI4 Rn ˛

(3)

The H value is estimated using the bulk aerodynamic resistance equation: H=

a Cp dT rah

(4)

where a is the air density (kg m−3 ); Cp is the specific heat of dry air (1004 J kg−1 K−1 ); dT (K) is the temperature gradient between two heights z1 (∼0.1 m) and z2 (∼2 m) above the canopy layer; and rah is the aerodynamic resistance (s m−1 ) to heat transport between z1 and z2 . METRIC computes dT for each pixel by assuming that dT scales linearly with surface temperature: dT = b + aTs

(5)

where a and b are image-specific empirical parameters estimated using two end-pixels (hot and cold extreme pixels) where H values can be reliably assigned. As rah and H are both unknown, METRIC applies the Monin–Obukhov theory in an iteration procedure with an initial rah value for neutral atmospheric conditions. The iteration procedure ends when dT and rah at the hot extreme pixel converge, then H for each pixel can be computed and the instantaneous ET calculated using Eq. (1). 2.1.2. Ts -VI triangle model The Ts -VI triangle model introduced by Jiang and Islam (1999) is a simple model to estimate surface ET over large heterogeneous areas using only remote sensing data. ET is calculated based on:



␭ET = ϕ (Rn − G)

 +



(6)

where  is the slope of saturated vapor pressure versus air temperature (kPa ◦ C−1 ) and  is the psychrometric constant (kPa ◦ C−1 ). ϕ is a complex-effect parameter that accounts for the effects of aerodynamic and canopy resistances (dimensionless). Although ϕ looks similar to the ␣ parameter (∼1.26) in the Priestley–Taylor equation, it encompasses a wide range of evaporative conditions with values ranging from 0 to ( + ␥)/. The pixel-by-pixel ϕ value can be detected from contextual information of an image with a Ts /fc feature space presented by Jiang and Islam (2001) and Tang et al. (2011) using the two-step

J. Lian, M. Huang / Agricultural Water Management 165 (2016) 153–162

linear interpolation scheme. The surface evaporative fraction (EF) can be expressed as EF = ϕ

+

(7)

The instantaneous ET can then be computed by substituting Rn , G, and EF calculated from Eqs. (2), (3), and (7) into Eq. (6). 2.1.3. SSEB model The SSEB model (Liu et al., 2010b; Senay et al., 2007) estimates ET by adjusting the spatially explicit maximum reference ET using the scaled ET fraction (ETf) from thermal imagery, similar to the concept of CWSI (Crop Water Stress Index) proposed by Jackson et al. (1981). Here, ETdaily = ETf × ETm

(8)

and ETf =

Ts,hot − Ts,i Ts,hot − Ts,cold

(9)

where ETm is the maximum ET for the region (mm); the reference ET (ETr ) calculated using meteorological data monitored at the Daman superstation and the Penman–Monteith equation (Allen et al., 1998) is usually used as ETm ; and Ts,i , Ts,hot , and Ts,cold represent the surface temperature of pixel i, the hot extreme pixel, and the cold extreme pixel (K), respectively. 2.1.4. Selection of extreme pixels The same hot and cold extreme pixels were selected for all models in order to compare model performance with respect to computing ET values. The “cold” pixel was selected from wellwatered irrigated land with a relatively low surface temperature, where the NDVI value was greater than 0.7 and the ˛ value ranged from 0.18 to 0.25 (Allen et al., 2013). At this pixel, ETcold is presumed to be 1.05ETr and Hcold = Rn ,cold − G cold − 1.05ETr . In contrast, the “hot” pixel was selected from dry bare land with a relatively high surface temperature, where NDVI < 0.1. At this pixel, EThot was assumed to be zero and Hhot = Rn ,hot − Ghot . 2.1.5. Daily and monthly ET estimations Daily ET data of the satellite overpass date are commonly obtained by extrapolating instantaneous ET values using the constant EF method (Sugita and Brutsaert, 1991) and constant reference ET fraction (ETr F) method (Allen et al., 2007b). The constant EF method assumes the daily EF equals the instantaneous EF calculated at the satellite overpass time, and daily G is ignored. Specifically, ETdaily = EF × Rn,daily =

␭ET × Rn,daily Rn − G

(10)

where Rn ,daily is the ground measured daily net radiation (W m−2 ). ETr F is the ratio of estimated ET to ETr , and the constant ETr F method hypothesizes that the daily ETr F equals the instantaneous ETr F at the satellite overpass time using: ETdaily = ETr F × ETr,daily =

ET × ETr,daily ETr,inst

(11)

where ETr ,inst (mm h−1 ) and ETr ,daily (mm d−1 ) are the instantaneous and the daily reference evapotranspiration rates of the overpass time, respectively, calculated using the Penman–Monteith equation (Allen et al., 1998). Monthly ET is calculated using the method proposed by Allen et al. (2011), by summing the daily ET values over a month. Daily ET of the non-overpass date is calculated by multiplying the daily ETr by the pixel-wise ETr F, which is interpolated from ETr F maps

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obtained on two adjacent overpass dates on a pixel-by-pixel basis. Specifically,

ETmonth =

n 

ETdaily,i =

i=1

n 

ETr Fi × ETr,daily,i

(12)

i=1

where n is the total days of a month and i is the ith day of a month.

2.2. Study area and data sources 2.2.1. Study area The Heihe River Basin (HRB) is the second largest inland river basin in China and is located in the arid north-west part of the country. Its middle stream is a typical oasis-desert landscape with high diversity; it is the most developed area at the regional scale (Eziz et al., 2010; Liu et al., 2010a). The landscape structure in the area is a result of water resource distribution. Irrigated farmland is distributed along the river and is surrounded by desert. The transition zone located between the oases and deserts plays a critical role in maintaining the stability of the oasis ecosystem (Zhao and Zhao, 2014). Shrub land, sparse forest land, and medium and low coverage grasslands are sparsely distributed in isolated patches in this zone (Li et al., 2001). The large contrast between the surface characters and strong advection of oasis and desert are acknowledged in earlier works (Jia et al., 2013; Li and Shao, 2014a). This study focuses on two administrative regions (Ganzhou District and Linze County) in the middle stream area (Fig. 1). The area is about 10,000 km3 , with altitude varying between 1360 and 2400 m (Li and Zhao, 2010). The area has a continental dry climate with a mean annual temperature of 7.6 ◦ C and mean annual precipitation of 100–250 mm. The irrigation received by lands planted with maize ranges from 600 to 840 mm (Li and Shao, 2014b).

2.2.2. Data sources A total of six cloud-free Landsat OLI/TIRS images (Path 133/Row 33) were obtained from the USGS Earth Resources Observation and Science Center (http://glovis.usgs.gov/) for the 2013 growing season. The acquisition dates were DOY 106, 122, 154, 186, 202, and 282. The DEM map, the boundaries of the HRB, and administrative regions and land-use/land-cover data were downloaded from the Environmental & Ecological Science Data Center for West China, National Natural Science Foundation of China (http:// westdc.westgis.ac.cn). The parameters␣, NDVI, and ε0 were calculated based on the algorithm developed for earlier Landsat satellite using the corresponding bands (Sobrino et al., 2008; Tasumi et al., 2008). Surface temperature was first computed based on the splitwindow (SW) algorithm (Jimenez-Munoz et al., 2014) and then corrected using the digital elevation model (DEM) map to account for the influence of topography on Ts . The ground observations used in this study were obtained from the Heihe Watershed Allied Telemetry Experimental Research (HiWATER) project (Li et al., 2013; Liu et al., 2011). Five EC systems were installed in the region, with two sites (Daman superstationfarmland and Zhangye-wetland) located in the oasis area and three sites (Shenshawo, Huazhaizi, and Bajitan) in the surrounding desert area. An automatic weather stations (AWS) was also installed at each site. Table 1 shows the main soil and vegetative types for 5 sites, while Table 2 presents the installed sensors and their heights.

2.3. Data analyses The estimated ET values were compared with the measured values by the EC at each site. The mean absolute bias (Bias), root mean

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Fig. 1. Study area (a) location in China, (b) Landsat image, and (c) land-cover types.

Table 1 Summary of soil and vegetative types for five observation sites. Site

Land-cover type

Longitude (◦ E)

Latitude (◦ N)

Altitude (m)

Soil texture

Daman Zhangye Bajitan Huazhaizi Shenshawo

Farmland Wetland Gobi desert Desert steppe Desert

100.372 100.446 100.304 100.319 100.493

38.856 38.975 38.915 38.765 38.789

1556 1460 1562 1731 1594

Silt loam Silt loam Loamy sand loam Loamy sand

Table 2 Heights and orientations of installed eddy covariance (EC) system and climatic sensors at 5 sites. Site

EC system

Automatic weather station

Daman

4.50 m, north

Zhangye Bajitan Huazhaizi

5.20 m, north 4.60 m, north 2.85 m, north

Shenshawo

4.60 m, north

Air temperature/humidity

Wind speed

Wind direction

Air pressure

Four-component radiometer

3, 5, 10, 15, 20, 30, and 40 m, north 5 and 10 m, north 5 and 10 m, north 1, 1.99 and 2.99 m, north 5 and 10 m, north

3, 5, 10, 15, 20, 30, and 40 m, north 5 and 10 m, north 5 and 10 m, north 0.48, 0.98, 1.99 and 2.99 m, north 5 and 10 m, north

3, 5, 10, 15, 20, 30, and 40 m, north 10 m, north 10 m, north 4 m, north

2m

12 m, south

2m 2m In waterproof box

6 m, south 6 m, south 2.5 m, south

10 m, north

2m

6 m, south

square error (RMSE) and determination coefficient (R2 ) were used to evaluate the accuracy of the model.

n  i=1

Bias =



ETmodel,i − ETobs,i

n  i=1

ETmodel,i − ETobs,i

2 (14)

n

n  R =

(13)

n

RMSE =

2



i=1

n  i=1

ETmodel,i − ETmodel

ETmodel,i − ETmodel



ETobs,i − ETobs

2 n  i=1

2

ETobs,i − ETobs

2

(15)

3. Results and discussion 3.1. Comparison of the estimated and measured instantaneous surface fluxes To evaluate the performance of the three models for ET estimation, Rn and G were computed using the same methods for METRIC and the Ts -VI triangle model, while Rn and G estimations were not required for the SSEB model. Remote sensing based instantaneous available energy (AE) values equal to net radiation minus soil heat flux were overestimated with a bias of 44.76 W m−2 and a root mean square error (RMSE) of 73.09 W m−2 (Fig. 2). The overestimations

J. Lian, M. Huang / Agricultural Water Management 165 (2016) 153–162

Fig. 2. Comparison of the estimated (via remote sensing; RS) versus observed (Obs.) instantaneous available energy values (AE, W m−2 ).

were more frequent at low AE values, and the largest discrepancy occurred at the Wetland site on DOY 106. The equations that estimate Rn and G might cause significant errors at the beginning and end of the growing season when the surface characters are the most heterogeneous. dos Santos et al. (2011) found that the largest error (16%) in temporal variation of measured and SEBAL estimated Rn values occurred for low NDVI at a pasture site. Because the energy closure problem of EC measurements has been reported in many studies (Liu et al., 2011; Massman and Lee, 2002), instantaneous ET values were compared with modified ET values using the Bowen ratio closure method (Twine et al., 2000) (Fig. 3). Because ET was computed directly as the partition of the maximum ET (SSEB model) or AE (the Ts -VI triangle model) and H could then be deduced as the residual of the surface energy balance, comparison of the estimated and measured H values is not displayed. Good correlations for estimated versus observed ET values were obtained for METRIC and SSEB, with the R2 values of 0.92

157

and 0.90, respectively. The Ts -VI triangle model demonstrated poor performance (R2 = 0.78). The outlier when using the Ts -VI triangle model (Fig. 3c) occurred at the Wetland site on DOY 106 as a result of overestimated instantaneous AE values. This indicates that the Ts -VI triangle model is more sensitive to the estimated AE than METRIC, and is because METRIC is designed to compensate for bias in AE and H by using an image-based calibration procedure (Allen et al., 2007a). In terms of absolute error, SSEB had the best performance with a bias of 4.34 W m−2 . However, ET was underestimated in the high ET range (Fig. 3b), likely due to the ignored impact of albedo on available energy (Senay et al., 2011). Moreover, an inaccurate ETm value in Eq. (8) could cause appreciable errors in ET estimation.

3.2. Comparison of the estimated and measured daily and monthly ET values Daily ET was extrapolated using the ETr F method from instantaneous ET at the satellite overpass time estimated from METRIC and Ts -VI triangle model, while the SSEB model provided daily ET prediction directly. Similar to instantaneous ET, good agreements were obtained for METRIC and SSEB with RMSEs of 0.72 and 0.84 mm d−1 , respectively (Fig. 4). The outlier in the Ts -VI triangle model (Fig. 4c) led to a large RMSE of 1.50 mm d−1 . The constant EF method provided reasonable estimates of low daily ET values (Fig. 5), and a modest RMSE (0.70 mm d−1 ) was obtained for the Ts -VI triangle model. This means the constant EF method has the potential to compensate for errors in AE estimation. However, significant underestimation occurred for high ET values. Allen et al. (2007a) and Gonzalez-Dugo et al. (2009) reported that the EF method underestimated crop daily ET and the bias could be reduced when the ETr F method was used. Irmak et al. (2012) suggested a mixture use of ETr F and EF based on land-cover types.

Fig. 3. Comparison of the estimated and EC measured instantaneous latent heat fluxes (W m−2 ) for the (a) METRIC, (b) SSEB, and (c) Ts -VI triangle models.

Fig. 4. Comparison of daily ET (mm d−1 ) extrapolated using ETr F method with measured flux values for the (a) METRIC, (b) SSEB, and (c) Ts -VI triangle models.

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Table 3 Model performance statistics for monthly ET estimation from three models for different land-cover types. Land-cover type

Month

ET EC

METRIC (mm)

Ts -VI (mm)

ET

Absolute error

ET

Farmland

April May June July August September Mean

16.25 67.54 134.69 138.95 135.52 96.94

30.78 113.93 148.81 156.21 135.11 112.49 18.05

14.53 46.40 14.12 17.26 0.42 15.55

45.58 107.06 139.30 165.50 140.95 114.41 20.48

Wetland

April May June July August September Mean

38.02 111.36 208.00 190.67 187.12 170.52

74.17 171.73 164.40 176.12 170.57 152.00 31.62

36.15 60.36 43.61 14.55 16.55 18.52

141.66 278.25 206.51 182.43 176.90 159.37 50.27

Sandy desert

April May June July August September Mean

0.36 13.05 40.02 57.41 45.38 24.44

13.43 16.75 14.38 20.38 25.27 24.30 16.62

13.07 3.70 25.64 37.03 20.11 0.14

9.76 13.06 6.97 13.21 15.94 14.13 21.07

SSEB (mm) Absolute error

ET

Absolute error

34.87 99.05 129.61 145.06 122.33 96.10 12.56

18.62 31.52 5.08 6.11 13.19 0.85

103.64 166.89 1.49 8.24 10.22 11.15

85.11 181.68 155.41 153.18 145.43 127.57 48.69

47.09 70.31 52.59 37.49 41.69 42.96

9.40 0.02 33.05 44.20 29.45 10.31

7.23 12.14 8.67 15.06 16.34 13.00 20.33

6.87 0.91 31.36 42.35 29.04 11.43

29.32 39.52 4.610 26.55 5.430 17.47

in a 14.6% mean decrease in estimated H, which could further lead to increasing estimates of ET. This indicates that it would be preferable to select the cold extreme pixel from a water body when crops are in the initial stages of the growing season; a cold extreme pixel selected from irrigated farmland might not meet the ETr requirement. Similar trends with larger discrepancies were obtained for the wetland site in May, but no significant overestimation of monthly ET was observed at the desert site. This means that the selection of cold extreme pixels had a larger influence on ET estimation for the oasis area than for desert.

Fig. 5. Comparison of daily ET (mm d−1 ) extrapolated using the EF method and measured flux values for the (a) METRIC and (b) Ts -VI triangle models.

To assess the performance of the three models for monthly ET estimation, comparisons of estimated and measured monthly ET values are presented in Table 3. As similar temporal trends were evident for the Shenshawo, Huazhaizi, and Bajitan desert sites, statistics for only one are provided for comparison to the other two land-cover types. For the farmland site, all three models performed well with mean absolute errors ranging from 12.56 to 20.48 mm. For the wetland site, METRIC performed better (mean absolute error of 31.62 mm) than both SSEB and the Ts -VI triangle model (mean absolute errors of 50 mm). Overestimations of more than 100 mm for April and May were caused by the evidently overestimated daily ET on DOY 106 and DOY 122 for the Ts -VI triangle model. In contrast, the absolute errors ranged from 40 to 70 mm for all months for the SSEB model. Underestimations were observed at the Shenshawo site from June to August for all three models. The reason for this might be that the ET was mainly influenced by precipitation in the desert, and the use of clear-day images could not capture the rising trend of ET in this area. In addition, the low temporal resolution of Landsat images (16-day) may limit the precision of monthly or seasonal ET estimation. The largest monthly absolute error in farmland occurred in May, due to the warmer cold extreme pixel selected on DOY 122 when the vegetation fraction was relatively low. The Ts, cold was 296.01 K, while the mean water body surface temperature was 289.19 K. Long et al. (2011) reported that a 2 K increase in Ts, cold could result

3.3. Comparison of ET estimations for the three models To investigate the performance of the three models for different land-cover types, pixel-wise comparisons of instantaneous ET were made based on a typical image (dated 7/21/2013; DOY 202) when vegetation was in the middle of the growing season. Fig. 6 shows frequency histograms of ET from the three models for the three main land-cover types. Maize was the main crop cultivated in farmland, accounting for about 60% of the total area, with other crops (spring wheat, tomatoes, sugar beets) cultivated to a lesser extent (Han et al., 2014; Zhao et al., 2010). Importantly, these different crops have quite different phenological characteristics. For example, spring wheat had already been harvested but maize was in the middle stage of growing season on DOY 202. As a result, the instantaneous ET for farmland had values ranging from 50 to 600 W m−2 . Similar patterns were observed in farmland for all models, with mean values of 374.75, 370.78, and 392.16 W m−2 for the METRIC, SSEB, and the Ts -VI triangle models, respectively. Bimodal patterns (Fig. 6d–f) were obtained for the transition zone due to heterogeneous surface characteristics. The relatively high ET values (>150 W m−2 ) showed similar patterns for the three models and peaked at around 200 W m−2 . However, the METRIC output was different from those of the Ts -VI triangle model and SSEB for pixels with relative low instantaneous ET (<150 W m−2 ): ET focused at about 100 W m−2 and about 60 W m−2 for SSEB and the Ts -VI triangle model, respectively, while the frequency of ET increased steadily and reached a peak of ∼50 W m−2 for METRIC. ET values in desert ranged from 0 to 400 W m−2 for the three models with mean values of 131.81, 176.07, and 145.07 W m−2 for the METRIC, SSEB, and the Ts -VI triangle models, respectively

J. Lian, M. Huang / Agricultural Water Management 165 (2016) 153–162

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Fig. 6. Frequency histograms of instantaneous ␭ET (W m−2 ) for three main land-cover types estimated from the METRIC (the left three histograms), SSEB (the middle three histograms), and Ts -VI triangle (the right three histograms) models.

(Fig. 6g–i). Similar to the distributions observed for the transition zone, ET values estimated from the SSEB and Ts -VI triangle models were mainly concentrated at 170 and 120 W m−2 , respectively, while pixel numbers increased smoothly from 0 to a peak at ET ∼80 W m−2 for METRIC. Fig. 7 contains density plots of comparisons of the instantaneous ET (W m−2 ) estimated by the three models for the three main land-cover types. The R2 and RMSE values were calculated from 30,000 pixels randomly selected using ordinary linear regression. Good agreements were obtained for the instantaneous ET derived from the Ts -VI triangle model and METRIC for the three land-cover types, with all R2 values equal to or larger than 0.90. Particularly poor agreements were obtained for the ET estimations from SSEB and METRIC for the transition zone and desert, with R2 values of 0.66 and 0.69, respectively (Fig. 7e and f). Better agreements were obtained for the ET estimations from the SSEB and the Ts -VI triangle models across the three land-cover types (R2 of 0.87–0.95). For ET estimation in farmland, all comparisons presented good consistencies with RMSE values ranging from 13.69 to 24.38 W m−2 . However, greater ET values were estimated from the Ts -VI triangle

model (Fig. 7a and g). The overestimations of ET were likely from the warmer cold edge of well-watered farmland. The METRIC uses well-watered farmland and ETr to consider the advection effective of energy, while the Ts -VI triangle model does not account for regional advection. This suggests that different criteria for extreme pixel selection should be followed for different models. The cold edge should be determined using the surface temperature of water bodies for the Ts -VI triangle model. Compared to METRIC, the Ts -VI triangle and SSEB models overestimated ET for the low ET domain for the transition zone and for the whole domain for the desert area, with SSEB usually producing the largest ET values. The overestimation of ET by SSEB for bare land has been reported and corrected using NDVI by Senay et al. (2011). Comparisons of ET estimations from METRIC and SSEB with the NDVI correction are illustrated in Fig. 8. The ET values were globally reduced, and a better agreement with METRIC output was obtained for desert. This means that SSEB with the NDVI correction might be more suitable for desert area than the original SSEB model (Senay et al., 2011). However, ET in farmland is more related to the given ETm , a factor that should be calibrated for each specific study area (Senay et al., 2014).

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Fig. 7. Density plots of comparison of instantaneous ET (W m−2 ) for three main land-cover types. The top row corresponds to ET estimated from the Ts -VI triangle and METRIC; the middle row corresponds to ET estimated from SSEB and METRIC; and the bottom row corresponds to ET estimated from SSEB and the Ts -VI triangle model. The color coding refers to the frequency of data points at each location, with red for high frequency and blue for low frequency.

Simple contextual methods (the Ts -VI triangle model and SSEB) have the potential to provide ET estimations consistent with the complex physically-based METRIC model. However, ET estimations from SSEB and the Ts -VI triangle model are quite sensitive

to derived AE, Ts , EF, and ETm , while METRIC can compensate for errors in estimated AE and Ts by using the inverse calibration of two extreme points.

Fig. 8. Density plots of instantaneous ET (W m−2 ) estimated from SSEB and METRIC with NDVI correction for three main land-cover types. The color coding refers to the frequency of data points at each location, with red for high frequency and blue for low frequency.

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4. Summary and conclusions The performance of three contextual remote sensing based models was assessed using the EC measured ET values at different time scales during the growing season. For instantaneous ET, good correlations were obtained between the modeled versus measured instantaneous ET for METRIC and SSEB with the R2 values above 0.90. Outliers occurred when the available energy was overestimated by the Ts -VI triangle model. Comparisons of instantaneous ET on a pixel-by-pixel basis for the three models for three main land-cover types showed that the outputs of METRIC and the Ts VI triangle model for farmland were the most consistent, while the poorest agreements were obtained when comparing ET estimated from SSEB and METRIC. In addition, two methods to extrapolate ET to daily ET were evaluated using the EC measured daily ET. The results indicated that the ETr F method could be used for well-watered areas to recognize regional advection effects, while the EF method tended to give better outputs for other areas. Good performance for monthly ET prediction was obtained for farmland by all of the models with mean absolute errors ranging from 12.56 to 20.48 mm. The largest monthly absolute error in farmland appeared in May, which was attributed to the warmer cold extreme pixel selected on DOY 122. Overall, the METRIC model outperformed the SSEB and Ts -VI triangle models. METRIC modulated the error in ET estimation caused by biases in available energy and Ts by using the inverse calibration of two extreme points. The Ts -VI triangle model is both sensitive to available energy and derived EF, and large variations in ET estimation would be caused by ill-defined “cold” and “hot” edges. SSEB can give reasonable estimates for the low ET range with the NDVI correction, yet the underestimation for the high ET range remains; this may be improved by using a larger ETm . However, the ETm should be based on relevant prior knowledge. Finally, reasonable estimates can be achieved by carefully selecting extreme pixels or edges, and validation is required when applying remote sensing based models, especially contextual methods. Further insights with respect to the sensitivity of estimated ET to surface parameters and automatic extreme pixel selection procedures should be investigated for operational applications.

Acknowledgements This work was financed by the National Natural Science Foundation of China (No. 91025018). The authors thank the Heihe Plan Science Data Center, National Natural Science Foundation of China, for providing ground and near-surface measurements obtained in the HiWATER project.

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