# Evaluation and Aggregation Properties of Thermal Infra-Red-Based Evapotranspiration Algorithms from 100 m to the km Scale over a Semi-Arid Irrigated Agricultural Area

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## Abstract

**:**

^{2}located in a semi-arid irrigated agricultural zone in the northwest of Mexico. Wheat is the dominant crop, followed by maize and vegetables. The HR ASTER dataset includes seven dates between the 30 December 2007 and 13 May 2008 and the LR MODIS products were retrieved for the same overpasses. ET retrievals from HR ASTER products provided reference ET maps at LR once linearly aggregated at the km scale. The quality of this retrieval was assessed using eddy covariance data at seven locations within the 4 by 4 km

^{2}square. To investigate the impact of input aggregation, we first compared to the reference dataset all fluxes obtained by running TSEB and SEBS models using ASTER reflectances and radiances previously aggregated at the km scale. Second, we compared to the same reference dataset all fluxes obtained with SEBS and TSEB models using MODIS data. LR fluxes obtained by both models driven by aggregated ASTER input data compared well with the reference simulations and illustrated the relatively good accuracy achieved using aggregated inputs (relative bias of about 3.5% for SEBS and decreased to less than 1% for TSEB). Results also showed that MODIS ET estimates compared well with the reference simulation (relative bias was down to about 2% for SEBS and 3% for TSEB). Discrepancies were mainly related to fraction cover mapping for TSEB and to surface roughness length mapping for SEBS. This was consistent with the sensitivity analysis of those parameters previously published. To improve accuracy from LR estimates obtained using the 1 km surface temperature product provided by MODIS, we tested three statistical and one deterministic aggregation rules for the most sensible input parameter, the surface roughness length. The harmonic and geometric averages appeared to be the most accurate.

## 1. Introduction

^{−1}parameter.

^{−1}parameter used in the calculation of turbulent fluxes to relate the aerodynamic and surface temperatures [18].

^{2}on the instantaneous retrieval between the aggregated latent heat fluxes and the latent heat flux computed from surface average parameters at the km scale. On the other hand, the same authors have performed similar work on real data for a mixture of riparian trees and stressed shrubs [39] and a realistic contribution (fraction cover f

_{c}) of both patches to the LR pixel (with a contribution of the most extreme conditions of less than 20%). They concluded that divergence was significantly less than 50 W/m

^{2}, which is the typical precision of most Energy Balance (EB) models [40] for retrieving instantaneous latent heat flux. They also found that simple averaging of displacement height and an averaging of roughness length based on a lognormal to the power −2 reduced the bias down to less than 10 W/m

^{2}. Both studies pointed out the need to use proper efficient scaling relationships in parameter estimation at LR. There has been abundant literature on the subject from back in the 1990s, mostly based on theoretical works deriving deterministic [41] or statistical [42] relationships between local and regional parameters for land–atmosphere exchange modelling. For roughness length, Wassenaar et al. [43] conclude that a geometric averaging of the roughness length is performing best; this is also the scaling proposed by Taylor [44].

^{−1}parameter [48]; and (3) that the limited accuracy of height estimate (and subsequently the roughness length for momentum transfer) from RS data is rarely taken into account, with few empirical relationships that tend to diverge for high NDVI values [49]. The latter becomes more significant when LR RS data are used to derive surface roughness lengths. However, none of those aggregation rules (apart from [43]) have been evaluated with actual data acquired at LR on very heterogeneous land surfaces.

- To investigate ET flux scaling properties from HR to LR using data from the same sensor (i.e., ASTER), as well as data stemming from different sensors onboard the same platform (i.e., ASTER, MODIS).
- To develop and evaluate new and existing scaling relationships based on easily obtainable RS quantities to relate local HR and LR roughness lengths.

## 2. Data

#### 2.1. Study Area

^{3}. In this hydrological context, an accurate method to estimate water losses by ET is essential for managing the water resources at the regional scale. Between December 2007 and May 2008 an international field measurement campaign was set up on a 4 × 4 km

^{2}zone located in the South of Obregon city and an important HR and LR RS dataset covering the same period and area was collected.

#### 2.2. In Situ Measurements

^{2}square (Figure 1c). Half hourly global solar and atmospheric incoming radiations, air temperature and relative humidity as well as wind speed were recorded. Eddy covariance data was acquired at 2 to 3 m at seven sites located on different crop plots to represent the diversity of crop types and phenological stages as well as contrasted simultaneous soil water conditions related to irrigation patterns (Figure 2). At each site, net radiation, soil heat flux (at 0.05 m depth), surface temperature and soil moisture (at 0.05 and 0.3 m depth) were measured each 10 s before being averaged over 30 min periods. The latent and the sensible heat fluxes were acquired at a frequency of 10 Hz, processed using the FLUXNET guidelines [55] and converted to 30 min flux average. The devices used for all the automatic measurements at the different EC and meteorological stations as well as the fluxes quality analysis were described in Chirouze et al. [22].

#### 2.3. Remote Sensing Data

^{2}).

#### 2.4. Remote Sensing Data Preprocessing

^{2}. Therefore, in what follows, the aggregation performance for MODIS will be assessed at a more representative 2000 m spatial resolution instead of the usual 1 km resolution, in agreement with previous work on surface temperature disaggregation using the same dataset and on the same area [16].

## 3. Energy Balance Models Parameterization and ET Calculation

#### 3.1. Available Energy

_{n}) and the ground heat flux (G). The net radiation is estimated with the same equation [22]:

_{sw}and R

_{lw}are, respectively, the shortwave and longwave surface incoming radiation, α the albedo, ε the emissivity and T

_{surf}the radiative temperature of the surface. R

_{sw}is taken from the meteorological station and ${R}_{lw}=1.24\left({e}_{a}/{T}_{a}\right)\sigma {T}_{a}{}^{4}$, where e

_{a}and T

_{a}are the actual vapour pressure and the temperature of the air measured by the meteorological station. The ground heat flux (G) is estimated according to the SEBAL model formulation [4], which proved to be the more accurate in this context [22]:

#### 3.2. SEBS Model

_{n}− G − H, where H is the sensible heat flux.

_{a}is the aerodynamic resistance to heat transfer at the surface–atmosphere interface, u is the wind velocity at level z, k = 0.4 is the von Karman’s constant, d

_{0}is the displacement height (d

_{0}≈ h

_{c}× 2/3, h

_{c}being the crop height), z

_{0h}is the roughness length for heat transfer and z

_{0m}the roughness height for momentum transfer (z

_{0m}≈ h

_{c}× 0.123). T

_{a}and T

_{aero}are the temperature of the air at reference and aerodynamic levels, respectively, ρ is the density of the air and c

_{p}is the specific heat capacity of air. Ψ

_{m}and Ψ

_{h}are the stability correction functions for momentum and sensible heat transfer and L is the Monin–Obukhov length.

_{c}is the vegetation fraction cover (in a pixel), and f

_{s}the bare soil fraction cover with f

_{c}+ f

_{s}= 1. A

_{1}describes the vegetation aerodynamic properties, kB

_{s}

^{−1}the bare soil properties, and A

_{2}represents the interactions between vegetation and bare soil. All these terms are estimated as in Su et al. [19].

_{dry}and LE

_{wet}are the latent heat fluxes in dry and wet conditions, e

_{s}the saturation vapor pressure temperature T

_{a}, γ the psychrometric constant and Δ the slope of the saturation vapor pressure at temperature T

_{a}.

_{r}) is then computed to estimate LE as LE = Λ

_{r}LE

_{wet}:

#### 3.3. TSEB Model

_{c}and LE

_{c}are the sensible and latent heat fluxes at the vegetation/atmosphere interface and H

_{s}and LE

_{s}the same heat fluxes at the bare soil/atmosphere interface. T

_{c}and T

_{s}are, respectively, the vegetation and bare soil temperature, r

_{s}[21] is an additional resistance to describe the resistance to heat transfer in the ABL at the bare soil/atmosphere interface, and r

_{a}the atmospheric resistance to heat transfer at the surface–atmosphere interface is expressed according to MOST.

_{g}is the relative fraction of the vegetation that is green. Since LAI is estimated through the NDVI, which is an indicator of the green vegetation development, and f

_{g}is here fixed to 1.

_{c}by introducing LE

_{c}in potential conditions (Equation (14)) in Equation (11). When T

_{c}is known, T

_{s}can be computed from Equation (13) and then H

_{s}from its formulation detailed in Equation (12). Finally, LE

_{s}is calculated as the residual term of the soil energy balance (Equation (10)). If the resulting LE

_{s}is positive, the solution is reached and the hypothesis of an unstressed vegetation is considered as valid even if neither the soil or the vegetation evaporate at a potential rate. If the resulting LE

_{s}is negative, the unstressed vegetation assumption is challenged, so LE

_{c}value is decreased until LE

_{s}is equal to 0. Then, new H

_{s}and T

_{s}values are computed from Equations (10) and (12) and new T

_{c}, H

_{c}and LE

_{c}values from Equation (13), Equation (12) and Equation (11), respectively. If LE

_{c}is positive, a new solution is reached. In addition, if LE

_{c}is negative, the vegetation part is also considered as fully stressed and dry and LE

_{c}is set to 0. H

_{c}can then be computed from Equation (11) and a new T

_{c}value from Equation (12). T

_{s}can then be estimated according to Equation (13) and new H

_{s}and G values from Equation (12) and Equation (10), respectively.

#### 3.4. Daily ET Fluxes Generation

_{d}, we used an extrapolation algorithm based on an empirical diurnal shape of the evaporative fraction during a day in clear sky conditions (see [54]).

_{d}is the daily cumulative ET value, ET

_{i}the instantaneous evapotranspiration flux, which corresponds to the latent heat flux $E{T}_{i}=\frac{LE}{\lambda}$ (with λ being the latent heat of vaporisation), $EF=\frac{E{T}_{i}}{A{E}_{i}}$ is the evaporative fraction (considered as constant during daytime) defined as the ratio between the instantaneous ET value and the instantaneous available energy value, and AE

_{d}is the daily cumulative available energy computed as the daily cumulative net Radiation flux (R

_{nd}), considering that the cumulative soil heat flux at the daily scale can be neglected. R

_{nd}is estimated assuming that the R

_{nd}/R

_{ni}ratio has a sinusoidal evolution along the year as stated in Gomez et al. [58]:

_{ni}is the instantaneous net radiation flux, JD is the day of the year and a

_{1}, a

_{2}and a

_{3}are obtained for each hour of the day using mean local measurement to calibrate the relationship (not shown).

## 4. Methods

#### 4.1. General Design of the Experiments

- In a preliminary step, HR maps of ET were computed with both models from ASTER products (dataset named ‘HR-ASTER’ including spectral surface reflectances, spectral surface emissivities, radiative surface temperature and surface fluxes). ET maps were evaluated against the eddy correlation measurements performed in seven crop fields. These maps were aggregated at the kilometric resolution to be used in the following steps as a reference dataset to evaluate ET maps obtained at low resolution. This aggregation was done considering that surface fluxes can be averaged using a simple arithmetic mean. The reference dataset at low resolution was named ‘agg-ASTER’.
- In the second step, LR maps of ET were produced from the high-resolution ASTER products aggregated at the kilometric resolution (equivalent to MODIS resolution). LR RS products were used for all inputs of both models. This dataset was named ‘LR-ASTER’. ET maps at LR were evaluated against ‘agg-ASTER’ ET maps. Since both input datasets at LR and HR came from the same sensor, the biases between the two estimations of ET were only related to how the nonlinear relationships in the model translates the variability of inputs at HR into an average LR outputs that can be significantly different than the one generated using LR inputs.
- In a third step, LR maps of ET were produced from the MODIS products (surface temperature, emissivities, albedo, NDVI) at 2 km resolution, as it would be done in a standard application of SEBS and TSEB using MODIS data. These dataset (named ‘MODIS’) was evaluated against ‘agg-ASTER’ ET maps. In this case, differences between ET maps were related to a combination of the differences in products, input parameter derivations and heterogeneity/nonlinearity issues.
- In a fourth step, we analysed the possibility to derive SEBS and TSEB input parameters at low resolution by aggregating parameters estimated from high-resolution data. This scenario considered the possible use of high-resolution images in the solar domain from Earth observation satellites for deriving model inputs at the kilometric resolution. Decametric information are now increasingly available, in particular thanks to Sentinel2 satellites. We expected that this scenario would provide a deeper analysis of the potential source of biases in deriving ET and to develop more adequate aggregation rules for the relevant inputs.

#### 4.2. Estimating Surface Parameters at HR from ASTER Products

_{i}referred to the spectral reflectance from band i.

_{i}following Ogawa et al. [60]):

_{3N}) and red-VIS (ρ

_{2}) bands as:

_{c}) were estimated from NDVI values following [61]:

_{∞}= 0.94 and NDVI

_{0}= 0.14, and:

_{c}) were also estimated from NDVI values. Knowing the repartition of the different land use classes on the 4 × 4 km

^{2}square, it was clear that the majority of the area was covered by cereals. Hence, for each pixel (i), crop height was estimated as a linear regression between its temporal maximum and minimum NDVI values (respectively, NDVI

_{max}(i) and NDVI

_{min}(i)) and realistic maximum and minimum cereal crop heights’ values. The period covered by the ASTER dataset contained dates from the whole winter cereal growing period from seeding to harvesting. Therefore, the minimum height was that of a ploughed bare soil of 0.05 m equivalent height and a realistic maximum was set to 1.3 m, which led to:

_{om}using the simple rule of the thumb: z

_{om}(i) = 0.123 × h

_{c}(i).

#### 4.3. Estimating Surface Parameters at LR from ASTER Product

_{su}

^{4}, with σ = 5.67 × 10

^{−8}Wm

^{−2}K

^{−1}the Stefan–Boltzmann constant) before estimating the surface temperatures at LR by inverting the Stefan–Boltzman equation.

#### 4.4. Estimating Surface Parameters at LR from MODIS Product

_{c}. Albedo (blue sky value) was estimated from black-sky and white-sky MODIS values according to [62,63]:

_{BlackSky}(directional hemispherical reflectance) was the direct component and was a function of the solar zenith angle and α

_{WhiteSky}(bihemispherical reflectance) was the diffuse component. Black-sky and white-sky albedos corresponded to the extreme cases of purely direct or diffuse illumination. S is the fraction of diffuse solar radiation, which varied according to the atmospheric content in aerosol and water vapor and the solar zenith angle. S was fixed to 0.15 for all dates. The use of a constant value for S can introduce discrepancies in albedo and then in the available energy fluxes estimates. It could be estimated from MODIS aerosol product (MOD04-L2), but, in our area in dry season, it was usually low and had only a small impact on blue-sky albedo values. Broadband emissivity was computed from the emissivity products in band 31 and band 32 (${\epsilon}_{b31}\text{}and\text{}{\epsilon}_{b32}$) with the relationship detailed in Liang [64]:

#### 4.5. Aggregation Rules for the Input Parameters

_{i}is the relative pixel area of each individual roughness (or HR roughness). All three aggregation rules were implemented to derive effective input parameters at LR.

_{a}, the aerodynamic resistance in neutral conditions is a good approximation of the aerodynamic conditions with true stability corrections. In these conditions, the sensible heat flux expression reduces to:

_{a0}is the aerodynamic conductance to heat transfer at the surface–atmosphere interface in neutral conditions (inverse of the aerodynamic resistance r

_{a}

_{0}in the same conditions). If one assumed that, in those conditions, surface temperatures were similar at HR and LR, and our purpose was to find effective roughness values reducing as much as possible the difference between the HR and LR aerodynamic conductances g

_{a}

_{0}. The solutions were reached numerically by finding the effective (LR) surface roughness lengths that solves Equation (30):

_{a0i}is the aerodynamic conductance of HR pixel i, g

_{a0eff}the effective value at LR, and kB

^{−1}

_{eff}the effective kB

^{−1}, which allows deriving the effective roughness z

_{0meff}at LR (Equation (5)). Once computed, the effective surface roughness lengths were used as input into the models at low resolution together with the ‘LR-ASTER’ input dataset. The new ET maps were compared to the ‘agg-ASTER’ ET maps.

## 5. Results

#### 5.1. Preliminary Step: Evaluation of Flux Estimations at High Resolution from ASTER Data

_{c}(NDVI) and LAI(NDVI) relationships (Equations (20) and (21), respectively) were drawn empirically from the in situ measurements performed in [61]. A comparison to the same EC measurements showed an absolute relative bias lower than 1% for SEBS and about 20% for TSEB (see Figure 4). We thus considered the HR ASTER fluxes as realistic. Moreover, we checked that the available energy fluxes compared well to the measured values (relative bias of 5% and 9% for R

_{n}and G, respectively).

#### 5.2. Flux Estimation at Low Resolution from ASTER LR Data and MODIS Data

#### 5.2.1. Available Energy

_{n}and 0.04 (ASTER) and 0.002 (MODIS) for G. The relative bias is the mean relative difference between both estimates normalized to the mean value of the reference value (‘Agg-ASTER’ in our case). The corresponding Root Mean Square Error (RMSE) values were 0.03 mm·day

^{−1}for R

_{n}(ASTER and MODIS) and 0.09 mm·day

^{−1}(ASTER) and 0.11 mm·day

^{−1}(MODIS) for G. These good performances implied that, for both models, evaluating ET retrievals corresponded to evaluate their capacity to partition the available energy between sensible and latent heat fluxes.

#### 5.2.2. Estimation of ET from LR ASTER with SEBS

^{−1}.

#### 5.2.3. Estimation of ET from LR ASTER with TSEB

^{−1}, so that daily ET can be derived with a satisfying precision from LR inputs (Figure 6).

^{−1}) and the soil evaporation was lower (relative bias = −0.066 and RMSE = 0.38 mm·day

^{−1}). Compensation between evaporation and transpiration bias resulted in a very low bias for ET.

#### 5.2.4. Estimation of ET from MODIS Data with SEBS

^{−1}, which was quite similar to the results obtained with ‘LR-ASTER’ (in particular when considering RMSE). Again, the low biases at the seasonal scale did not reflect the date to date performances and, as for ‘LR-ASTER’, more contrasted results were obtained for the different vegetation development stages as shown on Figure 7. The resulting relative bias reached high values such as −0.32 on the 10 March 2008, −0.26 on the 11 April 2008 and 0.12 on the 13 May 2008.

#### 5.2.5. Estimation of ET from MODIS Data with TSEB

^{2}showed fairly good performances when TSEB was used to estimate ET with MODIS inputs: relative bias on daily ET was 0.03, RMSE 0.96 mm·day

^{−1}. However, these results were significantly less favourable than those obtained with ‘LR-ASTER’. Model performances regarding soil evaporation and transpiration separately were of similar magnitude as for the total flux when considering RMSE: 0.81 and 1.04 mm·day

^{−1}for daily evaporation and transpiration, respectively (Figure 8). As for the results obtained with LR ASTER, the transpiration calculated from MODIS input was higher than the aggregated HR fluxes (relative bias was 0.21) and the evaporation was lower (relative bias was −0.19). Again, compensation between evaporation and transpiration bias resulted in a lower bias for ET. As for the total flux (ET), transpiration and evaporation obtained from MODIS products presented higher discrepancies than from ‘LR-ASTER’ when compared to ‘agg-ASTER’.

#### 5.3. Test of Effective Roughness Length Parameterization at Low Resolution

#### Evaluation

^{−1}with LR ASTER and 0.78 mm·day

^{−1}with MODIS) and very low relative biases (0.03 and −0.02). The linear aggregation rule resulted only in slight reductions in RMSE and in biases (which, on average, were even increased). The geometric aggregation method gave RMSE on average only slightly higher and relative biases higher than the harmonic aggregation method. For all dates but the 27 April 2008 (low relative bias of 0.04), the relative biases were lower than the previous values obtained in Section 5.2.2. For each date, the relative biases were reduced. This was especially true for the dates that presented biases exceeding 10%.

## 6. Discussion

#### 6.1. Discussion on Flux Estimation at Low Resolution

- TSEB had significantly higher or similar scaling performances (flux conservation across scales) as SEBS, respectively, with LR ASTER data and MODIS data;
- SEBS had similar scaling performances with LR ASTER and MODIS data;
- TSEB scaling performances were significantly lower with MODIS data than with LR ASTER data (for ET mapping as well as for ET partitioning in E and T);
- With TSEB, relative biases between the soil and the vegetation offset each other when one considers the whole season.

_{om}, this is not the case for TSEB. In the latter, however, the aerodynamic temperature is tightly linked to the component (soil and vegetation) energy budgets and therefore very sensitive to the vegetation cover fraction f

_{c}. In our case, this translated into different evaporation/transpiration partitions across scales but did not much affect the total flux, which remained quite conservative across scales.

^{−1}term in Equation (6)). Roughness lengths values are derived from NDVI products coming from reflectances measured by two different sensors at different spatial resolutions. Both sensors will differ in their representation of the subscale heterogeneity and its associated vegetation pattern. It is also clear that the model sensitivity to the surface roughness lengths induces the high ET flux differences in the middle of the season when the heterogeneity is the most pronounced.

_{c}parameter.

^{−1}, respectively, for soil evaporation and transpiration fluxes), but ET was well estimated with MODIS data (see Figure 8).

_{c}values and, hence, biases in the available energy partition (R

_{nc}relative biases = −0.36 and −0.52; RMSE = 1.00 and 1.42 mm·day

^{−1}, respectively, for the 30 December 2007 and the 6 May 2008) that resulted in biases in transpiration between ‘agg-ASTER’ and MODIS instantaneous fluxes (LE

_{c}relative biases = 0.77 and 1.04; RMSE = 1.05 and 1.64 mm·day

^{−1}, respectively, the 30 December 2007 and the 6 May 2008). Biases on soil evaporation were smaller and did not offset the bias in transpiration on that particular day, but this did not affect the seasonal average performance of the TSEB model.

_{c}and roughness probability distributions between LR ASTER and MODIS using adapted maximum and minimum values of NDVI for MODIS could probably decrease this difference. Since the scaling analysis reies solely on the ‘LR-ASTER’ vs. ‘agg-ASTER’ intercomparison, the ‘MODIS’ vs. ‘agg-ASTER’ intercomparison is meant only to provide an illustration of a “real world” application of the models to moderate resolution data; therefore, the intermediate exercise consisting in matching MODIS and ‘agg-ASTER’ NDVI distribution while keeping MODIS LST was not considered in this study.

#### 6.2. Discussion on the Efficiency of Aggregation Rules

## 7. Conclusions

^{2}agricultural area were used to validate HR (100 m) ET maps computed with the SEBS and the TSEB models forced by ASTER data, local meteorological data and in situ measured crop heights in [22]. In order to bypass local crop height evaluation, we implemented a simple approach to derive crop heights (thus, indirectly surface roughness lengths) based on a priori maximum and minimum values scaled by NDVI levels. A common relationship valid for cereal covers in this area dominated by cereals or crops with similar height was derived. The performances of the SEBS and the TSEB models, when forced by remotely sensed vegetation height, were found to be similar to those obtained when in situ crop height measurements were used.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Study zone location in North America (

**a**); the Sonora state (

**b**); and the irrigated perimeter (

**c**).

**Figure 2.**Satellite view of the study zone with respective positions of the eddy covariance flux towers and their associated crop type (Imagerie© 2012 Cnes/Spot Image. DigitalGlobe. Données cartographiques© 2012 Google (City, US State abbrev., Country ; Inst. Nat. Estat. y Geog, INEGI).

**Figure 4.**Validation of SEBS (

**a**) and TSEB (

**b**) HR latent heat fluxes obtained using our simple approach to derive crop heights.

**Figure 5.**‘agg-ASTER’ (agg AST) and ‘LR-ASTER’ (LR AST) SEBS latent heat flux, along with ASTER NDVI (AST NDVI) time series.

**Figure 6.**(

**a**) ‘agg-ASTER’ and ‘LR-ASTER’ TSEB latent heat fluxes time series; (

**b**) partition between evaporation LE

_{s}and transpiration LE

_{v}.

**Figure 8.**(

**a**) ‘agg ASTER’ and MODIS TSEB latent heat fluxes time series; (

**b**) partition between evaporation LE

_{s}and transpiration LE

_{c}.

Sensor | Products | Frequency | Resolution [m] | Bands/Product/Subdatasets |
---|---|---|---|---|

ASTER | AST07XT—VNIR | 16 days | 15 | Band1 |

Band2 | ||||

Band3N | ||||

AST07XT—SWIR | 30 | Band4 | ||

Band5 | ||||

Band6 | ||||

Band7 | ||||

Band8 | ||||

Band9 | ||||

AST05 | 90 | Surface emissivity [-] | ||

AST08 | 90 | Surface temperature [°K] | ||

MODIS | MOD11A1 | Daily | ~1000 | Surface temperature [°K] |

Emissivity Band31 | ||||

Emissivity Band32 | ||||

QC_Day (Quality control) | ||||

MOD13A2 | 16 days | ~1000 | NDVI | |

VI Quality QA (Quality control) | ||||

MOD15A2 | 8 days | ~1000 | Lai_1 km | |

FparLai_QC (Quality control) | ||||

MCD43B3 | 16 days | ~1000 | Black Sky Albedo SW | |

White Sky Albedo SW |

**Table 2.**Relative biases for the ‘agg ASTER’ vs. ‘LR ASTER’ ET fluxes produced with SEBS at low resolution for different methods to estimate the LR surface roughness length parameter. z

_{om}—RS refers to the “remotely sensed” roughness length derived from LR NDVI values, “agg” uses aggregated values from HR to LR using the four methods (“lin”: linear, “geo”: geometric, “har”: harmonic, “grad”: deterministic averaging).

Date | ${\mathit{z}}_{\mathit{o}\mathit{m}}$—RS | ${\mathit{z}}_{\mathit{o}\mathit{m}}$—agg lin | ${\mathit{z}}_{\mathit{o}\mathit{m}}$—agg geo | ${\mathit{z}}_{\mathit{o}\mathit{m}}$—agg har | ${\mathit{z}}_{\mathit{o}\mathit{m}}$—grad |
---|---|---|---|---|---|

Relative bias [–] | |||||

30/12/2007(J364) | −0.10 | −0.10 | −0.06 | 0.05 | −0.15 |

23/02/2008(J54) | −0.11 | −0.09 | −0.05 | 0.00 | −0.07 |

10/03/2008(J70) | −0.20 | −0.15 | −0.09 | 0.00 | −0.17 |

11/04/2008(J102) | −0.11 | −0.09 | −0.07 | −0.01 | −0.08 |

27/04/2008(J118) | 0.02 | 0.00 | 0.01 | 0.05 | 0.00 |

06/05/2008(J127) | 0.13 | −0.10 | −0.08 | 0.10 | −0.02 |

13/05/2008(J134) | 0.07 | −0.07 | −0.06 | 0.06 | −0.10 |

Seasonal | −0.05 | −0.08 | −0.05 | 0.03 | −0.08 |

RMSE [mm/day] | |||||

30/12/2007(J364) | 0.74 | 0.62 | 0.44 | 0.36 | 1.09 |

23/02/2008(J54) | 1.49 | 1.08 | 0.88 | 0.70 | 1.34 |

10/03/2008(J70) | 1.48 | 1.11 | 0.76 | 0.57 | 1.61 |

11/04/2008(J102) | 1.01 | 0.75 | 0.56 | 0.34 | 1.03 |

27/04/2008(J118) | 0.48 | 0.33 | 0.28 | 0.42 | 0.45 |

06/05/2008(J127) | 1.12 | 0.60 | 0.55 | 0.65 | 1.26 |

13/05/2008(J134) | 0.79 | 0.54 | 0.55 | 0.47 | 1.27 |

Seasonal | 1.08 | 0.77 | 0.60 | 0.52 | 1.20 |

**Table 3.**Relative biases for the ‘agg ASTER’ vs. MODIS produced with SEBS at low resolution for different methods to estimate the LR surface roughness length parameter (the same symbols as Table 2).

Date | ${\mathit{z}}_{\mathit{o}\mathit{m}}$—RS | ${\mathit{z}}_{\mathit{o}\mathit{m}}$—Agg Lin | ${\mathit{z}}_{\mathit{o}\mathit{m}}$—Agg Geo | ${\mathit{z}}_{\mathit{o}\mathit{m}}$—Agg Harmonic | ${\mathit{z}}_{\mathit{o}\mathit{m}}$—Grad |
---|---|---|---|---|---|

Relative bias [-] | |||||

30/12/2007(J364) | 0.02 | 0.12 | 0.18 | 0.18 | 0.07 |

23/02/2008(J54) | −0.08 | 0.02 | 0.05 | −0.02 | −0.04 |

10/03/2008(J70) | −0.32 | −0.12 | −0.08 | −0.16 | −0.19 |

11/04/2008(J102) | −0.26 | −0.21 | −0.18 | −0.14 | −0.17 |

27/04/2008(J118) | −0.07 | −0.13 | −0.11 | −0.01 | −0.03 |

06/05/2008(J127) | 0.05 | −0.24 | −0.11 | 0.11 | 0.09 |

13/05/2008(J134) | 0.12 | −0.03 | 0.03 | 0.04 | −0.02 |

Seasonal | −0.10 | −0.09 | −0.04 | −0.02 | −0.06 |

RMSE [mm/day] | |||||

30/12/2007(J364) | 0.35 | 0.65 | 0.73 | 0.70 | 0.35 |

23/02/2008(J54) | 0.65 | 0.47 | 0.53 | 0.48 | 0.56 |

10/03/2008(J70) | 2.13 | 0.84 | 0.59 | 1.21 | 1.36 |

11/04/2008(J102) | 2.04 | 1.68 | 1.42 | 1.20 | 1.40 |

27/04/2008(J118) | 0.62 | 1.08 | 0.89 | 0.28 | 0.30 |

06/05/2008(J127) | 0.69 | 1.39 | 1.04 | 0.62 | 0.53 |

13/05/2008(J134) | 0.74 | 0.40 | 0.27 | 0.44 | 0.68 |

Seasonal | 1.23 | 1.03 | 0.86 | 0.78 | 0.85 |

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## Share and Cite

**MDPI and ACS Style**

Bahir, M.; Boulet, G.; Olioso, A.; Rivalland, V.; Gallego-Elvira, B.; Mira, M.; Rodriguez, J.-C.; Jarlan, L.; Merlin, O.
Evaluation and Aggregation Properties of Thermal Infra-Red-Based Evapotranspiration Algorithms from 100 m to the km Scale over a Semi-Arid Irrigated Agricultural Area. *Remote Sens.* **2017**, *9*, 1178.
https://doi.org/10.3390/rs9111178

**AMA Style**

Bahir M, Boulet G, Olioso A, Rivalland V, Gallego-Elvira B, Mira M, Rodriguez J-C, Jarlan L, Merlin O.
Evaluation and Aggregation Properties of Thermal Infra-Red-Based Evapotranspiration Algorithms from 100 m to the km Scale over a Semi-Arid Irrigated Agricultural Area. *Remote Sensing*. 2017; 9(11):1178.
https://doi.org/10.3390/rs9111178

**Chicago/Turabian Style**

Bahir, Malik, Gilles Boulet, Albert Olioso, Vincent Rivalland, Belen Gallego-Elvira, Maria Mira, Julio-Cesar Rodriguez, Lionel Jarlan, and Olivier Merlin.
2017. "Evaluation and Aggregation Properties of Thermal Infra-Red-Based Evapotranspiration Algorithms from 100 m to the km Scale over a Semi-Arid Irrigated Agricultural Area" *Remote Sensing* 9, no. 11: 1178.
https://doi.org/10.3390/rs9111178