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Evapotranspiration (ET) is normally considered as the sum of all water that evaporates from the soil and transpires from plants. However, accurately estimating ET from complex landscapes can be difficult because of its high spatial heterogeneity and diversity of driver factors, which make extrapolation of data from a point to a larger area quite inaccurate. In this paper, we hypothesize that MODIS products can be of use to estimate ET in areas of Caatinga vegetation, the hydrology of which has not been adequately studied. The experiment was conducted in a preserved level area of Caatinga in which meteorological and water flux measures were taken throughout 2012 by eddy covariance. Evapotranspiration estimates from eddy covariance were compared with remotely sensed evapotranspiration estimates from MOD16A2 and SAFER products. Correlations were performed at monthly, 8-day, and daily scales; and produced

The high equipment and maintenance costs involved in measuring water fluxes in agrosystems and natural ecosystems through field experiments make remote sensing an attractive alternative [

Evapotranspiration is normally considered as the sum of all water that evaporates from the soil and transpires from plants [

Spatial heterogeneity of ET can be great due to spatial variations in vegetation, weather, soils, and topography. As a result, extrapolation of ET estimates from flux towers to larger areas can be misleading [

Validation is used to analyze the uncertainties of model outputs, ensuring the accuracy of remotely sensed ET and enhancing its applications. A wide range of methods has been used, but in most cases, deviance measures and statistical tests are recommended ones. The first one evaluates the differences between the simulated and observed values [

In this paper, we hypothesize that MODIS products can be used to accurately estimate ET in areas of Caatinga vegetation in northeastern Brazil, which is a neglected Brazilian vegetation type in terms of research and investments [

The experiment was conducted in a preserved flat area of Caatinga (≈600 ha) located at Embrapa Semiárido research station of the state of Pernambuco, Brazil (40°19′16′′W, 9°02′33′′S; 350 m) (Figure

Location of the Flux tower installed in an area of Caatinga at Embrapa Semiárido, which is a research station of the state of Pernambuco, Brazil. Land use map source: PROBIO.

Meteorological and water flux measurements were taken throughout 2012 with sensors installed in a 16 m tower located in the study area. A net radiometer (model CNR-1, Kipp & Zonen B; V; Delft, Netherlands) installed at 13.3 m above the soil surface was used to determine incoming solar radiation (_{2}O analyzer (IRGA; model LI-7500, LI-COR Inc., Lincoln, NE, USA). All sensors were connected to a data logger (model CR1000, Campbell Scientific Inc., Logan, Utah, USA) set up to take measurements every 10 seconds. More information on the study site and monitoring system can be found in a previous paper [

MODIS MOD16A2 products were downloaded for all 8-day and month periods of the year of 2012 from ^{−1} or 0.1 mm month^{−1} to correct units (mm 8-day^{−1} or mm month^{−1}) by multiplication of all pixels by the 0.1, using the GDAL library (Geospatial Data Abstraction Library). The ET MOD16A2 dataset is composed of two components, (^{−2} day^{−1}), ^{−2} day^{−1}), ^{−3}), ^{−1 }K^{−1}), ^{−1}), and ^{−1}). The meteorological input data for that equation is always provided by the Global Modelling and Assimilation Office (GMAO) and includes daily total downward radiation (^{−2} day^{−1}), daily average air temperature (^{2}. These products are MOD12Q1 [

To create SAFER products, we used images of level 1B MOD021KM products from sensor Terra/MODIS for the year of 2012. Firstly, all 366 images were downloaded through the Level 1 and Atmosphere Archive and Distribution System (LAADS; ^{2}. The SAFER algorithm is basically a simplified and calibrated version of SEBAL [^{−2} sr^{−1 }^{−1}). For that, we used following equation:^{−2} sr^{−1 }^{−1}. ^{−1}), ^{−1}), ^{−1}), and _{0}), inputs are NDVI,

List of all MODIS imaged days of the year of 2012 used in the SAFER analysis. All these images were selected by having clear and high quality data for the pixel regarding an area of Caatinga at Embrapa Semiárido, which is a research station of the state of Pernambuco, Brazil (9°05′S; 40°19′W; 350 m).

01/07/2012 | 04/19/2012 | 05/31/2012 | 07/26/2012 | 10/20/2012 |

01/10/2012 | 04/26/2012 | 06/02/2012 | 07/31/2012 | 10/23/2012 |

01/28/2012 | 04/28/2012 | 06/06/2012 | 08/07/2012 | 10/26/2012 |

03/01/2012 | 04/29/2012 | 06/07/2012 | 08/08/2012 | 10/28/2012 |

03/02/2012 | 05/01/2012 | 06/09/2012 | 08/10/2012 | 10/29/2012 |

03/03/2012 | 05/03/2012 | 06/10/2012 | 08/11/2012 | 10/30/2012 |

03/04/2012 | 05/05/2012 | 06/15/2012 | 08/29/2012 | 12/14/2012 |

03/07/2012 | 05/07/2012 | 06/18/2012 | 09/04/2012 | 12/18/2012 |

03/09/2012 | 05/12/2012 | 06/20/2012 | 09/08/2012 | 12/20/2012 |

03/14/2012 | 05/14/2012 | 06/21/2012 | 09/14/2012 | 12/22/2012 |

03/17/2012 | 05/15/2012 | 06/22/2012 | 09/21/2012 | 12/25/2012 |

03/23/2012 | 05/16/2012 | 06/26/2012 | 09/25/2012 | — |

03/25/2012 | 05/17/2012 | 07/08/2012 | 09/26/2012 | — |

03/28/2012 | 05/29/2012 | 07/13/2012 | 10/03/2012 | — |

04/06/2012 | 05/30/2012 | 07/23/2012 | 10/10/2012 | — |

To estimate the reference evapotranspiration (^{−2} day^{−1}), ^{−2} day^{−1}), ^{−1}), ^{−1}), and ^{−1}). ^{−2} day^{−1}); ^{−2} day^{−1}); _{s} is the sunset hour angle (radians); ^{−2} day^{−1}); ^{−2 }min^{−1}); ^{−2} day^{−1}); ^{−2} day^{−1}); and ^{−4 }m^{−2} day^{−1}). The parameters ^{−1}) and RH is relative air humidity (%).

Covariance between SAFER and MOD16A2 and tower estimates of ET were analyzed using linear and nonlinear regressions. Normality and homoscedasticity of all ET data were tested with Shapiro Wilk test and Brown Forsyth test, respectively [

A first analysis of the weather data showed that, in general, global radiation (_{0}, which decreased to 76.6% of January’s (Figure _{0} is a modelled variable and varies positively in function of _{0} stable. November was again a rainy month that followed the same pattern as February, but since vegetation cover is lower in November than in February,

Meteorological scenario for the year of 2012 recorded by the Flux tower installed in an area of Caatinga at Embrapa Semiárido, which is a research station of the state of Pernambuco, Brazil. Global radiation is the monthly mean of accumulated daily incoming radiations; air, temperature, and relative humidity are presented as monthly mean of the daily mean; and rainfall is the monthly sum of all precipitations.

Monthly variation of all input parameters used in the SAFER algorithm for the year of 2012 in an area of Caatinga at Embrapa Semiárido, which is a research station of the state of Pernambuco, Brazil. NDVI, albedo, and Surface Temperature are presented as monthly mean of all available data and evapotranspiration is the monthly mean of all available data multiplied by the number of days in that month.

The ET estimates for the MODIS pixel of Caatinga in which the tower was located were compared with the observations

Monthly linear and exponential regression of MOD16A2 evapotranspiration (superior part) and SAFER evapotranspiration (inferior part) versus evapotranspiration from a Flux tower installed in an area of Caatinga at Embrapa Semiárido, which is a research station of the state of Pernambuco, Brazil, for the year of 2012.

The lower _{s} and

The exponential model performed better than the linear one for MOD16A2, indicating that the product’s ET estimates saturate and lose sensitivity at high ET rates. However, that is not a disadvantage of the SAFER algorithm. Since SAFER uses an exponential regression. This saturation pattern is based on an intrinsic behavior of the vegetation indexes used in both MOD16A2 and SAFER equations that are often over- or underestimated at low and high values for the Caatinga, respectively, and also on their relationships with LAI that has proven to be always exponential. For example, Costa et al. [

Linear estimation of ET using MOD16A2 produced a greater average residual (3.98 mm month^{−1}) than exponential one (2.82 mm month^{−1}). These results corroborate the NDVI-LAI relation that is better for nonlinear than linear equations. Also, the linear model violates assumptions of linearity and homoscedasticity. We can observe curvilinearity in the data, and residuals are greater for greater values of predicted ET (Figure ^{−1}) when compared with exponential estimates (2.43 mm month^{−1}).

Monthly regression standardized residuals versus regression standardized predicted values of all models. (a) and (b) are linear and exponential models for MOD16A2, respectively, and (c) and (d) are linear and exponential models for SAFER algorithm, respectively.

The relationship between observed ET and MOD16A2 estimates presented ^{−1}; Figure ^{−1}; Figure ^{−1} and 1.15 mm 8-day^{−1} for linear and exponential models, respectively (Figures

8-day linear and exponential regression of MOD16A2 evapotranspiration (superior part) and SAFER evapotranspiration (inferior part) versus evapotranspiration from a Flux tower installed in an area of Caatinga at Embrapa Semiárido, which is a research station of the state of Pernambuco, Brazil, for the year of 2012.

8-day regression standardized residuals versus regression standardized predicted values of all models. (a) and (b) are linear and exponential models for MOD16A2, respectively, and (c) and (d) are linear and exponential models for SAFER algorithm, respectively.

As monthly and 8-day SAFER linear models gave better results than the exponential ones, we decided to develop a linear model for daily ET. This model gave

Daily regression of SAFER evapotranspiration versus evapotranspiration from a Flux tower installed in an area of Caatinga at Embrapa Semiárido, which is a research station of the state of Pernambuco, Brazil, for the year of 2012. In the insets, dispersion pattern of residuals is relative to the model.

ET estimates of the SAFER algorithm were closer to Flux tower estimates than MOD16A2 estimates (Figure ^{−1} for SAFER in comparison to 11.08 mm month^{−1} for MOD16A2, and the mean 8-day differences were 0.019 and 2.89 mm 8-day^{−1} for SAFER and MOD16A2, respectively. However for the period between January and March, the differences were not as great: −0.012 mm month^{−1} and 0.17 mm 8-day^{−1} for SAFER compared to 16.36 mm month^{−1} and 4.31 mm 8-day^{−1} for MOD16A2. For the daily scale, the differences between SAFER and Flux tower ET estimates were 0.017 mm day^{−1} and 0.21 mm day^{−1} for the first and second periods, respectively. The SAFER model gave better results than the MOD16A2 model at all evaluated temporal scales. MOD16A2 tended to overestimate ET, due, we suggest, to the meteorological input data used in MOD16A2 algorithm. It is derived from a 1.00°

Monthly, 8-day, and daily variations of MOD16A2 and SAFER evapotranspiration and evapotranspiration from a Flux tower installed in an area of Caatinga at Embrapa Semiárido, which is a research station of the state of Pernambuco, Brazil, for the year of 2012.

SAFER linear ET models more closely matched Flux tower estimates of ET than all other models (Table _{0} instead of ET, which allows spatial extrapolation of ET [

Brief statistical summary and Root Mean Square Error (RMSE) of all nine evapotranspiration models.

Model | Product | Min and max obs. values (mm) | Min and max pred. values (mm) | RMSE (mm) |
---|---|---|---|---|

| Monthly MOD16A2 | 4.31 to 40.15 | 0.83 to 32.4 | 4.91 |

| 4.6 to 35.8 | 3.68 | ||

| Monthly SAFER | 4.5 to 28.94 | 1.97 | |

| 5.68 to 34.32 | 2.86 | ||

| ||||

| 8-day MOD16A2 | 0.83 to 18.95 | 0.33 to 12.17 | 2.18 |

| 1.07 to 16.47 | 1.99 | ||

| 8-day SAFER | 1.06 to 13.02 | 1.13 | |

| 1.49 to 23.3 | 2.27 | ||

| ||||

| Daily SAFER | 0.07 to 1.91 | 0.12 to 1.45 | 0.15 |

In this study, we compared ground-based ET with remotely sensed ET from MOD16A2 and SAFER products, and it produced

The authors declare that they have no competing interests.

The authors thank CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brazilian Coordination for the Improvement of Higher Level Personnel) for funding this study through the international project PVE A103/2013.