# Daily Evapotranspiration Estimations by Direct Calculation and Temporal Upscaling Based on Field and MODIS Data

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}, and a root-mean-square error (RMSE) of 18.6 W/m

^{2}; and (ii) the DC method underestimated daily ET by a smaller MBE of −4.8 W/m

^{2}and an RMSE of 22.5 W/m

^{2}. Therefore, the DC method has similar or better performance than the widely used constant EFr upscaling method and can estimate daily ET directly and effectively.

## 1. Introduction

## 2. Methodology

_{s}), surface net radiation (R

_{n}), and the soil heat flux (G).

#### 2.1. Direct Calculation Method

_{rad}) and aerodynamic (ET

_{aero}) terms to the overall ET with a decoupling coefficient connecting the equilibrium evapotranspiration (ET

_{eq}) and imposed evapotranspiration (ET

_{im}) by the surrounding air [39]:

_{rad}is the thermodynamic ET in which the energy is from the radiative energy (W/m

^{2}); ET

_{aero}is the aerodynamic ET which is decided by the aerodynamic factors (e.g., vapor pressure) (W/m

^{2}); ET

_{eq}is the equilibrium, or radiation-controlled ET (W/m

^{2}); ET

_{im}is the imposed, or stomatal-controlled ET (W/m

^{2}); R

_{n}is the surface net radiation (W/m

^{2}); G is the soil heat flux (W/m

^{2}); VPD is the vapor pressure deficit of the air (kPa); $\Delta $ is the ratio of vapor pressure and air temperature (kPa/°C); γ is the psychrometric constant (kPa/°C); λ is the latent heat of vaporization here taken as 2.45 MJ kg

^{−1}; $\rho $ is the air density (kg/m

^{3}); C

_{p}is the specific heat at constant pressure (J/(m·K)); and r

_{s}is the surface resistance (s/m).

_{eq}) and imposed evapotranspiration (ET

_{im}) according to the coupling of the surface atmosphere. It varies between the values ‘0’ and ‘1’, with 0 reflecting a perfect coupling in which the atmosphere provides all the energy for the ET while value 1 reflecting a perfect decoupling condition in which the radiation provides all the energy. Ω was calculated from remote sensing data based on its relationship with the crop water stress index (CWSI) [40]:

_{s}is the land surface temperature (K) and T

_{a}is the air temperature (K).

_{s}− T

_{a}) are computed based on the energy balance equation by assuming two extreme surface conditions: extremely dry and extremely wet. Under extremely dry conditions, all the available energy (R

_{n}− G) is utilized to heat the surface [H

_{dry}= ρC

_{p}(T

_{s}− T

_{a})/r

_{a}= (R

_{n}− G)]; the ET is almost zero and r

_{s}is large enough; and (T

_{s}− T

_{a}) reaches its maximum; otherwise, under extremely wet conditions, r

_{s}approaches zero and (T

_{s}− T

_{a}) reaches its minimum. Based on this, the theoretical minimum, and maximum values for (T

_{s}− T

_{a}) were computed with inputs of R

_{n}, G, aerodynamic resistance (r

_{a}, s/m), r

_{s}, and (e

_{a}* − e

_{a}), where e

_{a}* is the saturated vapor pressure at the evaporating front based on the air temperature (kPa); e

_{a}is the vapor pressure of the air above the canopy (kPa).

_{eq}and ET

_{im}based on Equations (2) and (3), using the decoupling coefficient combining them.

#### 2.2. Constant EFr Temporal Upscaling Method

_{2}is the wind speed at a height of 2 m (m/s); C

_{n}has different values at the daily and hourly time scales of 900 and 37, respectively [41]; C

_{d}equals different values at daytime and nighttime, 0.24 and 0.96, respectively [41]; and the remaining variables have the same definitions as those presented in the DC method.

_{a}and r

_{s}computed by combining three equations (Equations (12)–(14)). A detailed description of the theory and procedure can be found in previous studies [42].

#### 2.3. Retrievals of Satellite-Based Ts, R_{n}, and G

_{s}, K) [43], which is used as a parameter for the calculation of the decoupling coefficient (Ω) in Equation (4) and satellite-based surface net radiation. The surface net radiation is the sum of the downward and upward shortwave and longwave radiation at the ground:

_{g}and R

_{u}are the downward and upward shortwave radiations, respectively, W/m

^{2}; L

_{d}and L

_{u}are the downward and upward longwave radiations, respectively, W/m

^{2}; ${\epsilon}_{s}$ is the surface emissivity; ${\epsilon}_{a}$ is the atmospheric emissivity; and $\sigma $ is the Stefan–Boltzmann constant. $\alpha $ is the surface albedo retrieved with an empirical regression equation using MODIS surface reflectance products with band 5 removed (the subscript is the number of bands) [44]:

_{s}) products were applied to calculate the ratio of G to R

_{n}:

#### 2.4. Evaluation Metrics

^{2}, defined as follows) revealing their performances. Specifically, MBE is the mean-bias-error of the estimated data compared to the observed one, which is the amount of estimation bias with positive and negative values indicating higher and lower estimations, respectively; RMSE is the root-mean-square error from the comparison of estimated and observed daily ET; MAD is the mean-absolute difference from the comparison of estimated and observed values; and R

^{2}is the determination coefficient of the regression relationship between the estimated and measured quantities,

_{i}and OBS

_{i}are the daily ET estimations and observations; $\overline{EST}$ and $\overline{OBS}$ are the average values for the EST

_{i}and OBS

_{i}, respectively.

## 3. Materials

#### 3.1. Experimental Site

#### 3.2. Climatical and Flux Datasets

#### 3.2.1. Climatical and Radiation Variables

#### 3.2.2. Eddy Covariance Flux Measurements

_{2}/H

_{2}O gas analyzer (model LI-7500, Licor Inc., Lincoln, NE, USA) and a 3-D sonic anemometer/thermometer (model CSAT3, Campbell Scientific Inc., Logan, UT, USA). The measurement heights above the ground surface coincided with those of the climatic data. To measure these raw fluxes using the EC technique requires extensive data processing; thus, the measurements were checked with standard tools available in an open-source environment for processing high-frequency (10 or 20 Hz) data into half-hourly quality-checked fluxes with stationarity tests on covariances, flux calculations, and instrumental noise removal with conversions and corrections [45]. A series of data quality control procedures were performed to obtain a reliable EC-measured sensible heat flux and latent heat flux. In addition, according to the lower and upper limits of abnormalities, data spikes, and surface available energy, less than −100 W/m

^{2}or greater than 700 W/m

^{2}of these flux data were removed. The time scale of the flux data was one half-hour, which is consistent with that of climatic variables.

#### 3.3. Satellite Data

_{n}). The MOD11_L2 swath product was used to determine the land surface temperature (T

_{s}). The surface reflectance of spectral bands 1 through 7 from MOD09GA was employed to estimate the surface albedo and then the NDVI with the spectral reflectance in the red and near-infrared bands. The MOD03 product contains information on geodetic coordinates (latitude and longitude), solar zenith and azimuth angles, satellite zenith and azimuth angles, and ground elevation for each 1 km pixel, which was used for the geo-calibration of all MODIS data in this study. MOD35 was applied to select a clear sky day together with the measured solar radiation.

#### 3.4. Clear-Sky Selections and Energy Flux Correction

_{n}measurements, the EC measured LE with (the RE and BR corrections) and without correction of energy imbalance over 45 selected clear-sky days at 10:30 (corresponding to MODIS overpass time, recorded as instantaneous time), and daily scale are examined in Figure 3. For these selected days, the EC-measured LE at the 10:30 and daily scales were both considered as the largest energy component of the net radiation, and the measured LE closely followed the variation in the net radiation. Furthermore, the undermeasurements of LE at both instantaneous and daily scales were obvious. The closure ratio, which was used to reflect the degree of energy imbalance (defined as the ratio of the sum of H and LE to the surface available energy), averagely approximated 0.71 and 0.78 over the selected 45 days at the half-hourly and daily time scales, respectively.

## 4. Results and Analysis

#### 4.1. Evaluation Based on Field Data

#### 4.1.1. Evaluation with Original Flux Measurements

^{2}) of the daily ET estimations compared to the EC measurements are presented in Table 1.

^{2}, the MAD was 20.9 W/m

^{2}, and the RMSE was 25.6 W/m

^{2}, respectively; (iii) the constant Efr method had larger estimation deviations, with an MBE of 32.8 W/m

^{2}, an MAD of 32.8 W/m

^{2}, and an RMSE of 35.7 W/m

^{2}; (iv) the constant Efr method had greater overestimation (with a higher averaged MBE) and daily Ets were overestimated on all the selected clear days (MAD = MBE), whereas some underestimations related to the DC method occurred on part of selected days (MAD > MBE); and (v) the constant Efr method had a larger R

^{2}(0.926) than that of the DC method (0.879).

#### 4.1.2. Evaluation with Flux Measurements after Correction

^{2}) is much smaller than the corrected values, regardless if they were corrected with the BR (104.3 W/m

^{2}) or the RE (117.6 W/m

^{2}) schemes; thus, the undervalues of the daily ET measurements were further proved. Other statistical items related to the two estimation methods showed apparent differences when the estimation results were validated by corrected ET measurements using the RE and BR schemes.

^{2}, respectively; (ii) the DC method generated some underestimations of daily ET on a few selected days, as reflected by the larger difference between the MBE and MAD (7.4 and 16.1 W/m

^{2}, respectively); on the contrary, the constant EFr method still generated overestimations of daily ET on most selected days, shown by the small difference between the MBE and MAD (19.8 and 25.0 W/m

^{2}, respectively); (iii) both methods showed better results of daily ET estimation compared to that when validated using unclosed daily ET observations. A better performance of the DC method was noted, with the RMSE of 19.3 W/m

^{2}, compared to that of the constant EFr method with the RMSE of 29.7 W/m

^{2}; and (iv) both estimation methods showed similar R

^{2}(0.893 and 0.898) in the linear regressions of the validations and estimations.

^{2}, respectively; (ii) the DC method underestimated daily ET with a negative MBE (−4.7 W/m

^{2}), while the EFr method still had minimal overestimation of daily ET with positive MBE (10.5 W/m

^{2}); (iii) the similar value between the MBE and MAD (10.5 and 13.7 W/m

^{2}, respectively) of the constant EFr method further proved the overestimation on most selected days; and (iv) the constant EFr method had a larger R

^{2}(0.940) than that of the DC method (0.890).

#### 4.2. Evaluation Based on Satellite Data

#### 4.2.1. Estimation of Associated Parameters

_{n}, a, and G were retrieved and estimated. The estimations of these parameters based on MODIS data at satellite overpass times of 45 selected clear days were compared with ground-based measurements in our previous study [21]. MODIS-based Ts was compared with the temperature estimated from the measurements of upwelling and reflected downwelling longwave radiation because of the very limited spatial representativeness of the point-based Ts measurements. The bias (MODIS-based Ts minus ground-based Ts) and RMSE for the Ts estimation were 1.1 and 1.9 K, respectively, showing its high estimation accuracy. The bias and RMSE for the validation of the estimated R

_{n}according to Equation (15) were 15.2 and 45.7 W/m

^{2}, respectively, showing good agreement with the ground-based measurements. The soil heat flux was calculated as a fraction of the surface net radiation, according to Equation (17), and then the surface available energy (surface net radiation minus soil heat flux) at the MODIS pixel scale was obtained and compared with ground measurements. The bias and RMSE for the validation of the estimated surface available energy were 4.4 and 37.6 W/m

^{2}, respectively, revealing a good agreement between the estimated and ground-measured values.

_{ae}), decoupling coefficient (Ω) and surface resistance (r

_{s}) were then calculated. With the good performances of MODIS-based parameters guaranteeing confidence and reliability, together with the measurements of air humidity (e

_{a}) and air temperature (T

_{a}) representing the atmospheric conditions, the instantaneous ET were estimated and daily ET were obtained by direct calculation with the DC method and by temporal upscaling with the constant EFr method.

#### 4.2.2. Instantaneous ET Estimation with MODIS Data

^{2}and an average RMSE of 37.6 W/m

^{2}.

#### 4.2.3. Evaluation of Daily ET Based on Remote Sensing Data

^{2}) provided in Figure 8.

^{2}, respectively. The large difference between the MBE of 5.6 W/m

^{2}and the MAD of 15.2 W/m

^{2}revealed some underestimation of daily ET on a few selected days; (ii) daily ET was underestimated through the DC method, and the related MBE, RMSE, and MAD were −4.8, 22.5, and 19.0 W/m

^{2}, respectively. Similarly, the large difference between the MBE of −4.8 W/m

^{2}and the MAD of 19.0 W/m

^{2}also indicated some overestimation related to the DC method; (iii) the R

^{2}from the constant EFr method was 0.901, a little larger than that from the DC method, 0.878. Overall, the DC method had similar MBE and RMSE compared to the EFr method, which is already widely applied in the extrapolation of instantaneous ET based on remote sensing data.

_{n}, and G estimations.

## 5. Discussion

_{n}measurements, rather than daily available energy (R

_{n}− G), were utilized in this study because the soil heat flux was generally assumed to be zero on a daily scale, which may be negligible in the application and can cause some estimated deviations. Other studies [26] have recommended that the average daily G should not be ignored, and whether the accuracy will be improved by considering the average daily G should be further tested. For the validation of the results, the primary source was usually considered to be from the scale mismatch between the ET data sets; namely, the spatial representativeness of the EC-derived ET is different with a MODIS pixel resolution of 1 km. In this study, the test area is topographically flat, the vegetation extends uniformly within the footprint area, and the footprints of the measured flux data are overall all within the MODIS pixel; therefore, the uncertainty caused by the footprint from the EC measurements is relatively small.

## 6. Conclusions

^{2}with RMSEs ranging from 16.2 to 35.8 W/m

^{2}; as for the DC method, the MBEs ranged from −4.7 to 17.9 W/m

^{2}, with the RMSEs of 15.0–20.9 W/m

^{2}. It is concluded that (i) the DC method outperformed the constant EFr method when the results were compared with those obtained using unclosed measurements, (ii) the DC method still performed better with reduced overestimation compared with corrected EC measurements by the RE scheme, and (iii) the constant EFr method outperformed the DC method after the ET measurements were corrected by the BR scheme. With satellite data as input, good agreement between the daily ET estimations and EC measurements showed that both the DC and constant EFr methods performed well. The constant EFr method slightly overestimated daily ET and the DC method underestimated daily ET, with MBE values of 5.6 and −4.8 W/m

^{2}, RMSE values of 18.6 and 22.5 W/m

^{2}, and MAD values of 15.2 and 19.0 W/m

^{2}, respectively.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Tanny, J. Microclimate and evapotranspiration of crops covered by agricultural screens: A review. Biosyst. Eng.
**2013**, 114, 26–43. [Google Scholar] [CrossRef] - Jiang, S.; Wei, L.; Ren, L.; Xu, C.Y.; Zhong, F.; Wang, M.; Zhang, L.; Yuan, F.; Liu, Y. Utility of integrated IMERG precipitation and GLEAM potential evapotranspiration products for drought monitoring over mainland China. Atmos. Res.
**2021**, 247, 105141. [Google Scholar] [CrossRef] - Granata, F. Evapotranspiration evaluation models based on machine learning algorithms—A comparative study. Agric. Water Manag.
**2019**, 217, 303–315. [Google Scholar] [CrossRef] - Li, Z.L.; Tang, R.; Wan, Z.; Bi, Y.; Zhou, C.; Tang, B.; Yan, G.; Zhang, X. A review of current methodologies for regional evapotranspiration estimation from remotely sensed data. Sensors
**2009**, 9, 3801–3853. [Google Scholar] [CrossRef] [PubMed][Green Version] - Srivastava, A.; Sahoo, B.; Raghuwanshi, N. Evaluation of Variable Infiltration Capacity model and MODIS-Terra satellite-derived grid-scale evapotranspiration. J. Irrig. Drain Eng.
**2017**, 143, 1. [Google Scholar] [CrossRef][Green Version] - Bhattarai, N.; Wagle, P. Recent advances in remote sensing of evapotranspiration. Remote Sens.
**2021**, 13, 4260. [Google Scholar] [CrossRef] - Chen, J.M.; Liu, J. Evolution of evapotranspiration models using thermal and shortwave remote sensing data. Remote Sens. Environ.
**2020**, 237, 111594. [Google Scholar] [CrossRef] - Bastiaanssen, W.G.M.; Menent, M.; Feddes, R.A.; Holtslag, A.A.M. A remote sensing surface energy balance algorithm for land (SEBAL): 1. Formulation. J. Hydr.
**1998**, 212–213, 198–212. [Google Scholar] [CrossRef] - Bastiaanssen, W.G.M.; Pelgrum, H.; Wang, J.; Ma, Y.; Moreno, J.F.; Roerink, G.J.; Van der, W.T. A Surface Energy Balance Algorithm for Land (SEBAL): Part 2 validation. J. Hydr.
**1998**, 212–213, 213–229. [Google Scholar] [CrossRef] - Norman, J.M.; Kustas, W.P.; Humes, K.S. Source approach for estimating soil and vegetation energy fluxes in observations of directional radiometric surface temperature. Agric. Meteorol.
**1995**, 77, 263–293. [Google Scholar] [CrossRef] - Mu, Q.Z.; Heinsch, F.A.; Zhao, M.S.; Running, S.W. Development of a global evapotranspiration algorithm based on MODIS and global meteorology data. Remote Sens. Enviro.
**2007**, 111, 510–526. [Google Scholar] [CrossRef] - Farquhar, G.D.; von Caemmerer, S.; Berry, J.A. A biochemical model of photosynthetic CO
_{2}assimilation in leaves of C 3 species. Planta**1980**, 149, 78–90. [Google Scholar] [CrossRef][Green Version] - Tang, R.; Li, Z.L.; Tang, B. An application of the Ts–VI triangle method with enhanced edges determination for evapotranspiration estimation from modis data in arid and semi-arid regions: Implementation and validation. Remote Sens. Environ.
**2010**, 114, 540–551. [Google Scholar] [CrossRef] - Tang, R.; Li, Z.L. An end-member-based two-source approach for estimating land surface evapotranspiration from remote sensing data. IEEE Trans. Geosci. Remote Sens.
**2017**, 55, 5818–5832. [Google Scholar] [CrossRef] - Kumar, M.; Raghuwanshi, N.S.; Singh, R. Artificial neural networks approach in evapotranspiration modeling: A review. Irrig. Sci.
**2011**, 29, 11–25. [Google Scholar] [CrossRef] - Issaka, A.I.; Paek, J.; Abdella, K.; Pollanen, M.; Huda, A.K.S.; Kaitibie, S.; Goktepe, I.; Haq, M.M.; Moustafa, A.T. Analysis and calibration of empirical relationships for estimating evapotranspiration in Qatar: Case study. J. Irrig. Drain Eng.
**2017**, 143, 05016013. [Google Scholar] [CrossRef] - Kim, S.; Kim, H.S. Neural networks and genetic algorithm approach for nonlinear evaporation and evapotranspiration modeling. J. Hydr.
**2008**, 351, 299–317. [Google Scholar] [CrossRef] - Srivastava, A.; Sahoo, B.; Raghuwanshi, N.S.; Chatterjee, C. Modelling the dynamics of evapotranspiration using Variable Infiltration Capacity model and regionally calibrated Hargreaves approach. Irrig. Sci.
**2018**, 36, 289–300. [Google Scholar] [CrossRef] - Srivastava, A.; Kumari, N.; Maza, M. Hydrological response to agricultural land use heterogeneity using variable infiltration capacity model. Water Resour. Manag.
**2020**, 34, 3779–3794. [Google Scholar] [CrossRef] - Kalma, J.D.; McVicar, T.R.; McCabe, M.F. Estimating land surface evaporation: A review of methods using remotely sensed surface temperature data. Surv. Geophys.
**2008**, 29, 421–469. [Google Scholar] [CrossRef] - Ryu, Y.; Baldocchi, D.D.; Black, T.A.; Detto, M.; Law, B.E.; Leuning, R.; Miyata, A.; Reichstein, M.; Vargas, R.; Ammann, C.; et al. On the temporal upscaling of evapotranspiration from instantaneous remote sensing measurements to 8-day mean daily-sums. Agric. For. Meteorol.
**2012**, 152, 212–222. [Google Scholar] [CrossRef][Green Version] - Crago, R.D. Conservation and variability of the evaporative fraction during the daytime. J. Hydr.
**1996**, 180, 173–194. [Google Scholar] [CrossRef] - Xu, T.; Liu, S.; Xu, L.; Chen, Y.; Jia, Z.; Xu, Z.; Nielson, J. Temporal upscaling and reconstruction of thermal remotely sensed instantaneous evapotranspiration. Remote Sens.
**2015**, 7, 3400–3425. [Google Scholar] [CrossRef][Green Version] - Delogu, E.; Olioso, A.; Alliès, A.; Demarty, J.; Boulet, G. Evaluation of multiple methods for the production of continuous Evapotranspiration estimates from TIR remote sensing. Remote Sens.
**2021**, 13, 1086. [Google Scholar] [CrossRef] - Brutsaert, W.; Sugita, M. Application of self-preservation in the diurnal evolution of the surface energy budget to determine daily evaporation. J. Geophys. Res. Atmos.
**1992**, 97, 18377–18382. [Google Scholar] [CrossRef] - Delogu, E.; Boulet, G.; Olioso, A.; Coudert, B.; Chirouze, J.; Ceschia, E.; Le Dantec, V.; Marloie, O.; Chehbouni, G.; Lagouarde, J.P. Reconstruction of temporal variations of evapotranspiration using instantaneous estimates at the time of satellite overpass. Hydrol Earth Syst. Sci.
**2012**, 16, 2995–3010. [Google Scholar] [CrossRef][Green Version] - Alfieri, J.G.; Anderson, M.C.; Kustas, W.P.; Cammalleri, C. Effect of the revisit interval and temporal upscaling methods on the accuracy of remotely sensed evapotranspiration estimates. Hydrol. Earth Syst. Sci.
**2017**, 21, 83–98. [Google Scholar] [CrossRef][Green Version] - Jiang, L.; Zhang, B.; Han, S.; Chen, H.; Wei, Z. Upscaling evapotranspiration from the instantaneous to the daily time scale: Assessing six methods including an optimized coefficient based on worldwide eddy covariance flux network. J. Hydr.
**2021**, 596, 126135. [Google Scholar] [CrossRef] - Liu, Z. The accuracy of temporal upscaling of instantaneous evapotranspiration to daily values with seven upscaling methods. Hydrol. Earth Syst. Sci.
**2021**, 25, 4417–4433. [Google Scholar] [CrossRef] - Tang, R.; Li, Z.L.; Sun, X. Temporal upscaling of instantaneous evapotranspiration: An intercomparison of four methods using eddy covariance measurements and MODIS data. Remote Sens. Environ.
**2013**, 138, 102–118. [Google Scholar] [CrossRef] - Trezza, R. Evapotranspiration Using a Satellite-Based Surface Energy Balance with Standardized Ground Control. Ph.D. Thesis, Utah State University, Logan, UT, USA, 2002; p. 339. [Google Scholar]
- Allen, R.G.; Luis, S.; Pereira, D.R.; Martin, S. Crop Evapotranspiration-Guidelines for computing crop water requirements, FAO Technical Paper 56. FAO Rome
**1998**, 300, D05109. [Google Scholar] - Almorox, J.; Grieser, J. Calibration of the Hargreaves–Samani method for the calculation of reference evapotranspiration in different Köppen climate classes. Hydrol. Res.
**2016**, 47, 521–531. [Google Scholar] [CrossRef][Green Version] - Colaizzi, P.D.; Evett, S.R.; Howell, T.A.; Tolk, J.A. Comparison of five models to scale daily evapotranspiration from one-time-of-day measurements. Trans. ASAE
**2006**, 49, 1409–1417. [Google Scholar] [CrossRef] - Chávez, J.L.; Neale, C.M.U.; Prueger, J.H.; Kustas, W.P. Daily evapotranspiration estimates from extrapolating instantaneous airborne remote sensing et values. Irrig. Sci.
**2008**, 27, 67–81. [Google Scholar] [CrossRef] - Kaya, Y.Z.; Zelenakova, M.; Üneş, F.; Demirci, M.; Hlavata, H.; Mesaros, P. Estimation of daily evapotranspiration in Košice City (Slovakia) using several soft computing techniques. Theor. Appl. Climatol.
**2021**, 144, 287–298. [Google Scholar] [CrossRef] - Fan, J.; Yue, W.; Wu, L.; Zhang, F.; Cai, H.; Wang, X.; Lu, X.; Xiang, Y. Evaluation of SVM, ELM and four tree-based ensemble models for predicting daily reference evapotranspiration using limited meteorological data in different climates of China. Agric. For. Meteorol.
**2018**, 263, 225–241. [Google Scholar] [CrossRef] - Jiang, Y.; Jiang, X.; Tang, R.; Li, Z.L.; Zhang, Y.; Huang, C.; Ru, C. Estimation of daily evapotranspiration using instantaneous decoupling coefficient from the MODIS and field data. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2018**, 11, 1832–1838. [Google Scholar] [CrossRef] - McNaughton, K.G.; Jarvis, P.G. Predicting effects of vegetation changes on transpiration and evaporation. In Water Deficits and Plant Growth; Kozlowski, T.T., Ed.; Academic Press: Cambridge, MA, USA, 1983; Volume VII, pp. 1–47. [Google Scholar]
- Boegh, E.; Soegaard, H.; Hanan, N.; Kabat, P.; Lesch, L. A remote-sensing based study of the NDVI–Ts relationship and transpiration from sparse vegetation in the Sahel based on high-resolution satellite data. Remote Sens. Environ.
**1999**, 69, 224–240. [Google Scholar] [CrossRef] - Allen, R.G.; Walter, I.A.; Elliott, R.; Howell, T.A.; Itenfisu, D.; Jensen, M.E. The ASCE Atandardized Reference Evapotranspiration Equation. American Society of Civil Engineers. 2005. Available online: https://epic.awi.de/id/eprint/42362/1/ascestzdetmain2005.pdf (accessed on 20 January 2018).
- Boegh, E.; Soegaard, H.; Thomsen, A. Evaluating evapotranspiration rates and surface conditions using Landsat TM to estimate atmospheric resistance and surface resistance. Remote Sens. Environ.
**2002**, 79, 329–343. [Google Scholar] [CrossRef] - Tang, B.; Li, Z.L. Estimation of instantaneous net surface longwave radiation from MODIS cloud-free data. Remote Sens. Environ.
**2008**, 112, 3482–3492. [Google Scholar] [CrossRef] - Tasumi, M.; Allen, R.G.; Trezza, R. At-surface reflectance and albedo from satellite for operational calculation of land surface energy balance. J. Hydrol. Eng.
**2008**, 13, 51–63. [Google Scholar] [CrossRef] - Mauder, M.; Foken, T. Documentation and Instruction Manual of the Eddy-Covariance Software Package TK3 (Update). UNIVERSITÄT BAYREUTH Abt. Mikrometeorologie. 2015. Available online: https://epub.uni-bayreuth.de/2130/1/ARBERG062.pdf (accessed on 20 January 2018).
- Foken, T. The energy balance closure problem: An overview. Ecol. Appl.
**2008**, 18, 1351–1367. [Google Scholar] [CrossRef] - Anderson, M.C.; Norman, J.M.; Diak, G.R.; Kustas, W.P.; Mecikalski, J.R. A two-source time-integrated model for estimating surface fluxes using thermal infrared remote sensing. Remote Sens. Environ.
**1997**, 60, 195–216. [Google Scholar] [CrossRef] - Jiang, Y.; Tang, R.; Jiang, X.; Li, Z.L. Impact of clouds on the estimation of daily evapotranspiration from MODIS-derived instantaneous evapotranspiration using the constant global shortwave radiation ratio method. Int. J. Remote Sens.
**2019**, 40, 1930–1944. [Google Scholar] [CrossRef] - Gentine, P.; Entekhabi, D.; Chehbouni, A.; Boulet, G.; Duchemin, B. Analysis of evaporative fraction diurnal behaviour. Agric. For. Meteorol.
**2007**, 143, 13–29. [Google Scholar] [CrossRef][Green Version] - Niel, T.G.V.; Mcvicar, T.R.; Roderick, M.L.; Dijk, A.I.J.M.V.; Renzullo, L.J.; Gorsel, E.V. Correcting for systematic error in satellite-derived latent heat flux due to assumptions in temporal scaling: Assessment from flux tower observations. J. Hydrol.
**2011**, 409, 140–148. [Google Scholar] [CrossRef] - Tang, R.; Li, Z.L. An improved constant evaporative fraction method for estimating daily evapotranspiration from remotely sensed instantaneous observations. Geophys. Res. Lett.
**2017**, 44, 2319–2326. [Google Scholar] [CrossRef]

**Figure 1.**Flowchart of daily ET estimation and validation procedures through the DC method and the constant EFr method.

**Figure 2.**Location map of the Yucheng experimental site (

**a**) and land cover classification near the Yucheng site in 2009 from Global Land Cover Map in Google Earth Engine (

**b**) (Yuchen site was indicated by the filled red triangle and Shandong province was labeled as light blue).

**Figure 3.**Time-series of LE and R

_{n}observations with and without energy imbalance corrections over the Yucheng site at (

**a**) the instantaneous 10:30 scale and (

**b**) the daily scale over 45 clear skies.

**Figure 4.**Validations of daily ET estimations calculated by the DC method and temporal upscaled by the constant Efr method against with the original ET measurements.

**Figure 5.**Validations of daily ET estimations calculated by the DC method and temporal upscaled by the constant EFr method against with corrected EC flux measurements by (

**a**) the RE scheme and (

**b**) the BR scheme.

**Figure 6.**Validation of instantaneous ET estimations based on MODIS data, with the ET measurements corrected by the BR scheme.

**Figure 7.**Validations of daily ET estimations calculated directly by the DC method and temporal upscaled by the EFr method, based on MODIS data against with corrected ET measurements by the BR scheme.

**Figure 8.**Statistical items for daily ET estimations calculated directly by the DC method and temporal upscaled by the EFr method based on MODIS data against with corrected ET measurements by the BR scheme.

**Figure 9.**Temporal variations in daily ET calculated directly by the DC method and temporal upscaled by the EFr method against with ET measurements corrected by the BR scheme, during different crop (winter wheat and summer corn) growth stages.

**Table 1.**Statistical items of daily ET estimations calculated by the DC method and temporal upscaled by the constant EFr method, validated with uncorrected and corrected EC measurements.

Measurements (W/m^{2}) | MBE (W/m^{2}) | RMSE (W/m^{2}) | MAD (W/m^{2}) | R^{2} | ||
---|---|---|---|---|---|---|

Uncorrected | DC | 94.9 | 17.9 | 25.9 | 20.9 | 0.879 |

EFr | 32.8 | 35.8 | 32.8 | 0.926 | ||

Corrected with the RE scheme | DC | 104.3 | 7.4 | 19.3 | 16.1 | 0.893 |

EFr | 19.8 | 29.7 | 25.0 | 0.898 | ||

Corrected with the BR scheme | DC | 117.6 | −4.7 | 18.2 | 15.0 | 0.860 |

EFr | 10.5 | 16.2 | 13.7 | 0.940 |

^{2}is the determination coefficient of the regression relationship between the estimated and measured quantities.

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## Share and Cite

**MDPI and ACS Style**

Jiang, Y.; Wang, J.; Wang, Y. Daily Evapotranspiration Estimations by Direct Calculation and Temporal Upscaling Based on Field and MODIS Data. *Remote Sens.* **2022**, *14*, 4094.
https://doi.org/10.3390/rs14164094

**AMA Style**

Jiang Y, Wang J, Wang Y. Daily Evapotranspiration Estimations by Direct Calculation and Temporal Upscaling Based on Field and MODIS Data. *Remote Sensing*. 2022; 14(16):4094.
https://doi.org/10.3390/rs14164094

**Chicago/Turabian Style**

Jiang, Yazhen, Junrui Wang, and Yafei Wang. 2022. "Daily Evapotranspiration Estimations by Direct Calculation and Temporal Upscaling Based on Field and MODIS Data" *Remote Sensing* 14, no. 16: 4094.
https://doi.org/10.3390/rs14164094