# Modeling Surface Energy Fluxes over a Dehesa (Oak Savanna) Ecosystem Using a Thermal Based Two-Source Energy Balance Model (TSEB) I

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## Abstract

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^{−2}).

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Two-Source Energy Balance Model (TSEB)—Basic Formulations

_{RAD}) is a combination of soil (T

_{S}) and canopy (T

_{C}) temperatures, weighted by the vegetation fraction:

_{C}is affected by the sensor viewing angle (φ). The angular variation of directional emissivity was neglected because variations of less than 0.005 were obtained between viewing angles at nadir and 60° for most vegetated surfaces [17]. The fractional cover was derived from leaf area index (LAI) approximating f

_{C}at nadir view angle (when φ = 0) using an exponential function suggested by Choudhury [29].

_{S}) and canopy (subscript

_{C}) components separately:

_{C}and Rn

_{S}were computed considering the divergence of the short-wave and long-wave radiation separately, following Kustas and Norman [12]. Net short-wave radiation for the soil and the canopy was estimated following Campbell and Norman [30]. Net long-wave radiation was calculated as suggested by Ross [31], assuming an exponential extinction law of radiation in canopy air-space.

_{S}is the time in seconds relative to solar noon. A represents the maximum value of the ratio G/Rn

_{S}, assumed to have a constant value of 0.35 [29,33,34], C (s) is the peak in time position, supposed equal to 3600 following Cellier et al. [35], and B (s) is set to be equal to 74,000 [21].

_{C}, H

_{S}, and H were expressed as:

_{AC}is the air temperature in the canopy–air space (K), T

_{A}is the air temperature (K), R

_{X}is the resistance to heat flow of the vegetation leaf boundary layer (s m

^{−1}), R

_{S}is the resistance to the heat flow in the boundary layer above the soil (s m

^{−1}), and R

_{A}is the aerodynamic resistance calculated from the stability-corrected temperature profile equations [36], using Monin–Obukhov Similarity Theory (MOST). A description of R

_{X}, R

_{S}, and R

_{A}resistances computation is presented in the following section, considering their importance for the flux estimation under the conditions of this study.

_{C}) was derived, using as initial assumption a potentially transpiring canopy following the Priestley–Taylor equation [37]:

_{PT}is the Priestley–Taylor coefficient, usually taken as 1.26 (-), f

_{g}is the green vegetation fraction (-), Δ is the slope of the saturation vapor pressure versus temperature (kPa K

^{−1}) and γ is the psychrometric constant (kPa K

^{−1}). If the vegetation is stressed, the Priestley–Taylor approximation, i.e., Equation (12), overestimates the transpiration of the canopy, which underestimates the canopy temperature. This in turn via Equation (1) typically results in an elevated soil temperature that causes too high a value of H

_{S}in Equation (4) resulting in LE

_{S}< 0. The condensation during daytime convective conditions is not physically possible, and therefore indicates vegetation water stress. An iteration process is invoked that reduces α

_{PT}until it yields a value of LE

_{S}> 0.

#### Aerodynamic Resistance Scheme and Wind-Speed Profile

_{A}, R

_{S}, and R

_{X}used to derive soil and canopy H, were calculated following Norman et al. [16] and Kustas and Norman [17]:

_{0}is the zero-displacement plane (m), ${z}_{0M}$ is the roughness length for momentum transfer (m), k

_{vk}is the Von Karman constant and Ψ

_{M}and Ψ

_{H}are the atmospheric stability functions for momentum and heat, derived following Dyer [38].

^{−1}K

^{−1/3}) and b′ (-) were taken from Kustas and Norman [17], as used in the work of Kondo and Ishida [39]:

^{−1}), was parameterized following an exponential extinction law [40] as follows:

_{C}(m s

^{−1}), was then given by:

^{1/2}m

^{−1}), following Norman et al. [16], s was the mean leaf size (m) and u

_{d0+z0M}was estimated following Equation (16), but using (d

_{0}+ z

_{0M}) (m) as the reference height;

#### 2.2. Modifications to TSEB Formulations and Parameters

#### 2.2.1. Roughness Length and Zero Plane Displacement Height (z_{0M} − d_{0})

_{0}= 2/3 h

_{C}and z

_{0M}= 1/3 h

_{C}, but, in this study, both parameters were initially estimated according to [41,42] as described below:

_{C}) is wind-speed at the canopy; ζ (h

_{C}) is a generalization of C

_{d}LAI (which accounts for foliage density); C

_{d}is the drag coefficient of the foliage elements (typically ~0.2); a″ is the vertical leaf area density, which, together with P

_{m}, the momentum shelter factor and C

_{d}, takes into account the vertical canopy structure [41]; ${u}_{*}$ is the friction velocity; and k

_{vk}is the Von Karman constant.

_{0}and z

_{0M}. The latter approach of [44], considers the tree structure and is more suitable for tall woody vegetation. This method uses observation data to fit the estimation of normalized displaced height and roughness length, related to frontal area index (FAI), which is calculated following Schaudt and Dickinson [46]. These estimates of z

_{0M}and d

_{0}were compared with “observed” d

_{0}and z

_{0M}derived from Las Majadas in-situ wind measurements [47,48]. To calculate d

_{0}and z

_{0M}, two wind-speed measurements u

_{1}and u

_{2}(m s

^{−1}) at height z

_{1}= 15 and z

_{2}= 9 (m) using cup anemometers, were combined with friction velocity, ${u}_{*}$ (m s

^{−1}) at z

_{U}= 15 (m) from the 3-D sonic anemometer. The 30-min average wind-speeds u

_{1}, u

_{2}and ${u}_{*}$ sampled at 10 Hz were combined in a set of expressions based on log law for wind in the surface layer for computing d

_{0}and z

_{0M}under neutral conditions following Rooney [47] and Nakai et al. [48]:

_{2}(z

_{2}) > u

_{1}avoiding light wind cases, were used. An analysis of the model sensitivity to the aerodynamic roughness parameters was additionally performed, by incorporating the range in the magnitudes of z

_{0M}and d

_{0}estimated from the approaches described above into TSEB, and evaluating the impact on the computed H and LE values. To verify the roughness-length parameters, assuming a logarithmic wind profile above the canopy, wind-speed estimations at 9 m were compared with measured wind-speed at the same height.

#### 2.2.2. Within-Canopy Wind-Speed Profile Scheme

_{d}is the drag coefficient, typically equal to 0.2 [40], and ${\alpha}_{*}^{2}$ is a dimensionless coefficient that considers the presence of the roughness sub-layer of the underlying vegetative surface, taking values between 1.0 and 2.0 [53]. This parameter was set to 1, following Massman [50], based on the wind profiles of different crops.

_{d}(m) is the crown bottom height, the factor β is equal to the one from Massman [50] and the parameter C

_{C}is defined as follows:

_{d}was set equal to 1/3 h

_{C}as Cammalleri et al. [21] suggested, on the hypothesis that for tall canopies the foliage occupies the upper 2/3 of the canopy height primarily.

#### 2.2.3. Within-Canopy Wind-Speed Profile Scheme Modified to Account for Different Vegetation Layers

^{−1}), is parameterized as in Equation (16), but using 0.05 (m) as the reference height as in:

_{0M}/d

_{0}for the tree canopy was estimated according to [44] and were constant depending only on the oak structure. Magnitudes of z

_{0M}/d

_{0}for the grass were estimated, according to Massman [41], as a function of grass LAI, which was variable during the period. Tree height (h

_{C}

_{(oak)}) was treated as a constant over time and the understory canopy variation of the nominal canopy height (h

_{C}

_{(grass)}) was estimated using a growth curve derived from LAI and maximum and minimum measured heights. Leaf size was also different depending on the layer (for the tree s = 0.05 m and the grass s = 0.01 m). For Massman [50] formulation, a similar approach was taken with different extinction coefficients for the tree and the grass layers.

#### 2.2.4. Priestley–Taylor Coefficient Evaluation

_{PT}) [37] directly conditions this initial transpiration approximation, defined as:

_{eq}is the equilibrium evaporation rate. Theoretically, air passing over a saturated surface will gradually decrease in saturation deficit until an “equilibrium” evaporation rate is reached [37,55,56]. α

_{PT}shows the relative significance of E to E

_{eq}and thus indicates the evaporative control. In this study, the Priestley–Taylor coefficient for the whole ecosystem (grass + trees + soil) was named as α

_{PTS}, for the canopy layer (grass + trees) α

_{PTC}, for the trees α

_{PTT}, and for the grass α

_{PTG}.

_{PT}(for the ecosystem) varies significantly with LAI, vapour pressure deficit (VPD), and soil moisture. For natural vegetation, under arid or semiarid conditions, the optimal canopy α

_{PT}coefficient assumed lower values on average than typically observed for crops and fell even further at high values of VPD (α

_{PTC}-[54]; α

_{PTS}-[5]). The α

_{PT}coefficient may also display seasonal variations [57], with minimum values occurring in midsummer, when radiation inputs are at their peak, and maximum values during the spring and autumn. Thus, adopting the standard α

_{PTC}= 1.26 would not be appropriate for the dehesa ecosystem, since some degree of canopy stress or reduction in LE

_{C}could be reached before the TSEB algorithm indicates α

_{PTC}values lower than this reference due to soil evaporation becoming less than zero. In other words, the TSEB model in its current form, might not detect reduced transpiration through a reduction in α

_{PTC}from the widely adopted initial value of 1.26 [54] due to the plant physiology.

_{PTS}coefficient (soil and canopy) and its behavior over this ecosystem (E/E

_{eq}) were tested, computing E

_{eq}as:

_{PTC}[58], but, in this case, with the low tree fractional cover, it was not possible to isolate the influence of the soil and the Priestley–Taylor coefficient was a bulk one. (2) Based on ground data, an attempt was made to evaluate the α

_{PTT}, taking only the trees into account, by assuming that during the summer the understory grass was dry and all the latent heat flux measured by the ECT system should come from tree transpiration. For the calculation of the α

_{PTT}Equation (40) was inverted with Rn

_{C}computed assuming an exponential extinction to the measured net radiation (Beer’s Law). (3) A statistical process was also performed to assess the α

_{PTT}value under the conditions of the study, applying the TSEB model to the ecosystem when only trees were actively transpiring and the understory was dry (during the summer), assuming a constant LAI for oaks (using ground-truth measurement over the area) using both: (a) a green fraction equal to 1; and (b) green fraction values derived from MODIS (f

_{g}< 1). It was analyzed using an optimization scheme similar to that of Agam et al. [54], iteratively running the TSEB with the radiometric temperature derived from the four-way radiometer (i.e., the up-welling longwave measurements), over a range of initial α

_{PTT}values ranging between 0.5 and 1.5, with increments of 0.05. After each run, modeled LE was compared to the measured flux, analyzing the results with the Root Mean Square Difference statistic. Monthly averages of half-hourly RMSD for each α

_{PTT}value were computed and evaluated. The best fit was taken as the optimal α

_{PTT}for the canopy.

#### 2.3. Ground Measurements (TSEB Inputs and Validation)

_{0M}and d

_{0}. Both experimental sites were used to estimate the energy stored within the biomass using a simple approach based on meteorological data. Due to the possibility to derive thermal information from the four-way radiometer located over Las Majadas, this site’s data (2007–2011) were used to perform the statistical analysis of the Priestley–Taylor coefficient and to derive Priestley–Taylor bulk coefficient. Measurements taken over Las Majadas during 2008 and 2009 were used to evaluate the different versions of TSEB. In-situ data collected over Santa Clotilde, from 2012 through 2014, were used to study the evolution and structure of the canopy and the annual cycle of vegetation phenology (leaf area index, fractional cover, and green fraction).

#### 2.3.1. Santa Clotilde

^{−3}. Significant parameters for the description of canopy structure were determined in-situ, such as oak leaf size (s = 0.02 m), canopy height (h

_{C}, with constant average tree height of 8.5 m, and a seasonal variation for the grass layer, with a maximum height of 0.7 m in April/May and dry in the summer and winter periods), average height of the first branch (FBH = 2 m), average diameter of the trees measured at breast height located at 1.3 m (DBH = 0.48 m) and crown width estimated with high spatial resolution images (CW = 7 m).

#### 2.3.2. Las Majadas del Tiétar

_{C}), derived with the same method as for Santa Clotilde, was found to be about 20%, identical to the value estimated previously by the site team at ECT footprint scale.

^{−3}. Soil depth is important, and it is much larger than 3 m. The climate is Mediterranean with continental influence, with a mean annual temperature of 16.7 °C and mean annual precipitation of ca. 650 mm with large inter-annual variability. The site is used for continuous grazing of extensive livestock with a low density of 0.3 cows/ha. During the driest summer months (July–September), most of the cattle is moved to nearby mountain grasslands.

^{2}g

^{−1}) and an estimate of foliage biomass from allometric relationships (based on DBH distribution from a survey of 244 trees in a 12.46 ha area surrounding the tower).

#### 2.3.3. Energy Balance Closure Error and Footprint

#### 2.3.4. Remotely Sensed Inputs for TSEB

_{g}, Equation (11)), involved in the computation of the canopy transpiration, was adjusted using remote sensing data, following the suggestions of Guzinski et al. [22], to reflect the current phenological conditions. Values of f

_{g}were estimated using vegetation indices (VI), as computed by Fisher et al. [72], with the NDVI and the enhanced vegetation index (EVI) obtained from MODIS sensor data. To compare in-situ derived f

_{g}values with those from the satellite, ground reflectance measurements of each vegetation layer, taken with an ASD FieldSpectroradiometer (FieldSpec 3, ASDInc.), were processed to simulate MODIS bands to compute the VIs. Each estimation of f

_{g}was weighted by the area occupied by each component within the ecosystem. This was only possible on three days on which spectral measurements were made over both oak and grass, in July 2013, May 2014 and June 2014. These VI values were then compared with the VI derived with MODIS, with daily coverage and 250 m of spatial resolution for the visible and near infrared bands (MOD09GQ and MOD13Q1 products).

_{OUT}) and downwelling (LW

_{DN}) longwave radiation using the following equation:

_{C}[73].

#### 2.4. Evaluation of TSEB Performance in the Dehesa

_{0}− z

_{0M}and the wind-speed profile used in each version of the model and the denomination given to each one, for a better understanding of the procedure:

## 3. Results

#### 3.1. Evaluation of the Ground Measurements and TSEB Inputs

#### 3.1.1. Evaluation of the Surface Energy Fluxes Measured at the EC Sites

^{−2}and 40 W m

^{−2}, respectively. Better ECB was observed during the summer and winter times. In Santa Clotilde, this can be due to less noise derived from rainfall events and condensation processes occurred during these periods. Lower values of LE were seen to be directly correlated with better closure balance, which, with this flux being very low during dry periods, could indicate higher uncertainty in LE measurement than in H. This is consistent with the Las Majadas analysis done by Perez et al. [75]. LE has two peaks, in the spring and autumn, related to the typical rainfall temporal distribution. However, the magnitude and timing of precipitations can vary significantly from year to year.

^{−2}, which is 3% of the available energy. Unfortunately, ground measurement of this component is difficult, and the small magnitude of the estimated values suggests that it is likely to be a relatively small term for this ecosystem. However, the storage term can be larger for other areas in the dehesa with higher tree ground coverage. For example, Kobayashi et al. [77] evaluated S for an oak savanna with fraction tree cover of 50% and the storage term accounted for on average 12% of the available energy over the daytime.

^{−1}km pixel size) Earth observation satellites.

_{C}and meteorological conditions need to be taken into account.

#### 3.1.2. Evaluation of the Remote Sensing Data Used to Derive TSEB Inputs

_{g}values for Santa Clotilde derived from MODIS and spectral data (Table 2), no definitive conclusions about the goodness of the adjustment of MODIS index could be drawn, due to the low number of samples and the possible mismatch between data footprint. Although it seems that the MODIS-derived indices are higher than the spectral-derived indices in summer and the opposite situation is found during spring. Even when the grass is completely dry, f

_{g}values derived from MODIS are still high (e.g., August 2013 = 0.81). f

_{g}derived from the satellite incorporates the effect of the evergreen vegetation along with the grass, but considering the low tree fractional cover in these ecosystems, a strong influence would not be expected. It may be that this parameter does not reflect phenological conditions during the dry period sufficiently accurately for these ecosystems, with considerable seasonal variations.

#### 3.2. Evaluation of TSEB Formulation

#### 3.2.1. Roughness Length and Zero-Plane Displacement Height

_{0}indicate that it was less influenced by the formulation selected than the roughness length, with an uncertainty of 25% for all the approaches. A sensitivity analysis of d

_{0}influence on TSEB was performed with d

_{0}values ranging from a minimum of 1.5 to maximum of 4 m. The results showed that the maximum variation in flux estimation caused by the value adopted for d

_{0}was less than 1 W m

^{−2}for LE and 4 W m

^{−2}for H.

_{0M}value (Table 3), which is smaller (x = 0.52 and σ = 0.3) than the one expected for this tall vegetation environment (~1), possibly due to the low fractional cover of the oaks.

_{0M}range (0.1 to 1 m) was used in the TSEB sensitivity analysis, as presented in Figure 4, resulting in a variation of 20 W m

^{−2}(20%) in the sensible heat flux, an order of magnitude larger when compared with d

_{0}. Variations in the value of z

_{0M}affect the computation of the resistances and wind-speed profile, and, as a result, the overall fluxes. A lower z

_{0M}would lead to a higher R

_{A}(Equation (13)), and also lower R

_{X}(Equation (19)), due to the increase in canopy wind-speed. This higher u

_{C}will result in a higher wind-speed at soil level, resulting in lower R

_{S}(Equation (14)). Consequently, a larger H

_{S}is expected while a higher R

_{A}but lower R

_{X}generally reduced h

_{C}because the value of R

_{X}is less influenced by the value of z

_{0M}and u

_{C}than R

_{A}or R

_{S}, with mean differences between the resistance values for z

_{0M}= 0.1 and z

_{0M}= 1 corresponding with 50 s m

^{−1}for R

_{A}, 20 s m

^{−1}for R

_{S}and less than 1 s m

^{−1}for R

_{X}.

_{0M}reached a threshold value, H RMSD reached a limit and higher z

_{0M}values do not increase the errors. For LE, during the summer (Figure 4), higher z

_{0M}values would reduce the error. Higher z

_{0M}facilitates the sensible heat flux transport, with a decrease in R

_{A}at the expense of latent heat flux, improving the simulation of low LE rates over the dry season.

_{0}and z

_{0M}(function of tree vertical and horizontal structure) and Massman formulation [41], which yielded good results in previous studies with herbaceous vegetation [16,17,21] for the grass understory d

_{0}and z

_{0M}, as a function of the LAI and the height.

_{0}and z

_{0M}with Raupach [44] (outside the canopy layer) using a simple logarithmic approach considering stability effects was 20%, with r

^{2}of 0.94 (Figure 5a). The errors were highly dependent on the fetch influencing the measurements, with significantly higher errors when the fetch was up to the first 100 m (Figure 5b). This low fetch reflects low wind-speeds and highly unstable conditions that can increase the error in the stability corrections algorithms significantly. Under these highly convective conditions, the stability-corrected logarithmic profile may not apply to the current stability formulations [38,78].

#### 3.2.2. Within-Canopy Wind-Speed Profile Scheme

#### 3.2.3. Within-Canopy Wind-Speed Profile Scheme with the Modification to Account for Different Vegetation (Grass and Tree) Layers

#### 3.2.4. Priestley–Taylor Coefficient Evaluation

_{g}= 1 was assumed. This was followed by incorporating a variable f

_{g}determined from remote sensing, to analyse the influence of the different vegetation conditions. The selection of a P-T coefficient value for oak trees focused on data collected during the summer and winter. However, it is interesting to examine the results of the interaction over the course of a year (Figure 8). Even over extended periods, mainly during the autumn and spring, values corresponded to the co-existence of two contrasting vegetation layers, which are contributing to ET, in this case oak trees and grasses. Comparison between LE observed and estimated for the dry period with Priestley–Taylor coefficient equal to 0.5 is RMSD = 55 W m

^{−2}, 0.9 RMSD = 60 W m

^{−2}, and 1.26 RMSD = 71 W m

^{−2}.

_{PT}= 0.5 either using f

_{g}= 1 or variable f

_{g}. However, there is little increase in the magnitude of RMSD for α

_{PT}between 0.5 and 0.9, and it is only when the standard value α

_{PT}= 1.26 is used, does the RMSD increase by ~10 W m

^{−2}to nearly 65 W m

^{−2}. This translates to approximately a 20% error in LE using either f

_{g}= 1 or a variable f

_{g}. Although the lowest RMSD for LE over the summer months corresponded to α

_{PT}= 0.5, even taking into account the green fraction, using α

_{PT}= 0.5 had the highest error from January through May. This can be caused by the combined effect of f

_{g}and α

_{PT}= 0.5 in reducing transpiration.

_{PTS}for a similar ecosystem was found to be about 0.9, 30% less than values associated with evaporation from green, well-irrigated and fertilized crops such as wheat [5]. In the forest, observational studies found that unstressed α

_{PTE}y was significantly lower than the typical value of 1.26. Some of these values found for temperate broad-leaved evergreen forest were: 0.99 [79], 0.65 [80], 0.93 [81], 0.61 [82], 0.64 [83] and 0.72 [84,85,86]. For a temperate broad-leaved forest a mean value of 0.82 ± 0.16 was found [58]. All these studies suggest that natural vegetation displays a value of α

_{PTT}that is lower than the standard for crops, reflecting the relatively conservative water-use tendencies of semiarid natural vegetation adapted to these environments. Considering previous studies and the results presented in this section, Priestley–Taylor coefficient value was modified to 0.9 for the whole ecosystem. In doing so, the RMSD values were reduced by ~10 W m

^{−2}for the summer period.

_{PTS}bulk monthly averages estimations (Figure 9 on bulk Priestley–Taylor) during the day, ranged from a maximum value of 0.85 in May to a minimum value of 0.2 in August. In this area, equilibrium LE is higher than or equal to LE, so that the coefficient will vary between 0 and 1. Mean standard deviation over the whole year was 0.32, with maximum values occurring in winter (~0.4) and minimum values occurring in the summer (~0.2). This is likely due to the existence of different sources of ET during winter months, with trees (mostly dormant), but some grasses are transpiring because water is available and due to soil evaporation during and after rains, which is when most of the precipitation occurs. In contrast, in the summer, there are extended dry periods with very little, if any, precipitation, with only oak trees actively transpiring. Monthly averages of α

_{PTC}during daytime conditions were computed using the net radiation of the canopy (Figure 9 on Canopy Priestley–Taylor). For the summer season (from July to September) with no or little senescent grass in the understory (due to dry soils and animal grazing) and very little, if any, soil evaporation, it was assumed that α

_{PTC}was only for the oak trees (α

_{PTT}). The average α

_{PTT}estimated was 0.85. Monthly average estimates of daytime α

_{PTC}(grass + trees = α

_{PTT}+ α

_{PTG}) outside of the summer period using Rn

_{C}(trees + grass) was 1.2 (~1.26), which is likely to be due to the influence of the grass understory and the evaporation on the total ET. As it is shown in Figure 9, P-T bulk coefficient displayed an indirect relationship with the VPD, as suggested by Baldocchi and Xu [5] and Agam et al. [54]. This response may be related to the physiological characteristics of the natural vegetation growing in arid and semiarid environments, but a future study integrating the influence of the grasses in the calculation has to be conducted. Even though an increase in VPD enhances transpiration by producing a steeper humidity gradient between the leaf and the atmosphere, it also initiates negative feedback on stomatal conductance, which leads to a reduction in transpiration [5].

#### 3.3. Evaluation of TSEB Performance in Savanna Ecosystem

_{PTC}values as defined in Table 1. To improve accuracy, and to test the assumption of a constant oak LAI and variable grass LAI, the LAI measured at Las Majadas during 2008 and 2009 was used, with a clumping factor at nadir view of 0.71. As model input (air temperature and humidity, incoming solar radiation, and wind-speed) and validation data (four surface energy fluxes), the dataset collected over the same period by the eddy covariance tower was used. The Priestley–Taylor coefficient finally selected was 0.9, with f

_{g}estimated using MODIS remote information. The roughness length formulation selected for the application of TSEB with Goudriaan [40] and Massman [50] wind profiles with the common formulation of the extinction coefficient (TSEB G and TSEB M) was that of Raupach [44]. When separate estimates of z

_{0M}/d

_{0}for the trees and grasses were required, because an extinction coefficient for each canopy layer was calculated (TSEB G

_{GT}and TSEB M

_{GT}), Raupach formulation [44] was employed for the oak (function of vertical and horizontal tree structure) and Massman formulation [50] for the grass (function of the LAI and the height).

_{M}, TSEB-G

_{R}, TSEB-G

_{GT}, TSEB-M

_{R}) except the Massman modified wind-speed profile (TSEB-M

_{GT}), which calculated an extinction coefficient for each canopy layer, tended to overestimate LE for low-medium values showing the opposite trend for H. This may be because even integrating the green fraction and reducing the α

_{PT}coefficient, during the dry periods without available water LE flux is so low as to approach zero. The original α

_{PT}coefficient = 1.26 resulted in TSEB overestimating LE during the whole year, especially in summer.

_{M}, TSEB-G

_{R}, and TSEB-M

_{R}are within the limits found by other authors for more uniform and homogeneous canopies [13,16,17,18], and is within the uncertainties of the measurement technique (~40 W m

^{−2}). It is worth noting that all the modified wind profile versions that accounted for the existence of different canopy layers with different extinctions coefficients yielded similar results. Both the Massman and Goudriaan models of with-in canopy wind profile yielded reasonable estimates of both fluxes, while Cammalleri et al. [21] found for a more uniformly structured/spaced tree crop (olive orchard) a slightly better performance using the Massman model.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Modified Goudriaan [40] wind-speed profile for the different canopy layers.

**Figure 2.**Location of experimental sites, and areas of dehesa ecosystem across Extremadura and Andalusia.

**Figure 3.**Typical diurnal fluxes from one of the experimental sites (Santa Clotilde) for the different seasons.

**Figure 4.**Sensible and latent heat flux RMSD (W m

^{−2}) at Las Majadas, obtained for a range of roughness lengths during the year. Blue lines are for the sensible heat flux RMSD. Grey lines for the latent heat flux RMSD.

**Figure 5.**(

**a**) wind-speed estimated and measured at 9 m on Las Majadas site; and (

**b**) in relation to the fetch.

**Figure 7.**Wind-speed estimated and measured at 5 m over Las Majadas using the modified wind profile (Equations (34)–(39)).

**Figure 8.**Latent heat flux RMSD (W m

^{−2}) modifying the Priestley–Taylor coefficient from 0.5 to 1.5 with constant f

_{g}and variable f

_{g}, for Las Majadas. The green/white area represent the width between the upper limit (α

_{PT}= 1.26) and the lower limit (α

_{PT}= 0.5) using f

_{g}= 1, and the yellow area shows the reduce amplitude integrating a variable f

_{g}calculated from MODIS (dashed curves).

**Figure 10.**Estimated TSEB fluxes using TRAD vs. observed values (ECTs): (

**a**) TSEB

_{MR}; and (

**b**) TSEB-G

_{M-PT}.

**Table 1.**Defining the acronyms for the different TSEB computations based on estimates of d

_{0}and z

_{0M}using Massman [41] for grass or combined grass-oak system, or Raupach [44] for oak or combined grass-oak system, wind-speed profile in the canopy layer using Goudriaan [40] or Massman [50] and α

_{PTC}= 1.26 or 0.9.

TSEB-G_{M} | TSEB-G_{R} | TSEB-M_{R} | TSEB-G_{GT} | TSEB-M_{GT} | TSEB-G_{M-PT} | |
---|---|---|---|---|---|---|

d_{0} − z_{0M} | ||||||

Massman [41] | x | x (grass) | x (grass) | x | ||

Raupach [44] | x | x | x (oak) | x (oak) | ||

Wind-speed profile | ||||||

Goudriaan [40] | ||||||

a | x | x | x | |||

a(oak)—a (grass) | x | |||||

Massman [50] | ||||||

β | x | |||||

β(oak)—β (grass) | x | |||||

α_{PTC} | ||||||

1.26 | x | |||||

0.9 | x | x | x | x | x |

**Table 2.**f

_{g}estimated from in-situ spectra using MODIS bands functions and f

_{g}estimated from MODIS products for Santa Clotilde.

Date | f_{g} from Spectral Information | f_{g} from MODIS | ||
---|---|---|---|---|

Oak | Grass | Oak + grass | Oak + grass | |

23 July 2013 | 0.73 | 0.75 | 0.75 | 0.81 |

23 July 2013 | 0.76 | 0.75 | 0.81 | |

20 October 2013 | 0.78 | 0.66 | ||

20 December 2013 | 1 | |||

7 April 2014 | 0.94 | |||

5 May 2014 | 0.98 | 0.98 | 0.74 | |

13 May 2014 | 0.87 | 0.9 | 0.74 | |

19 May 2014 | 1 | |||

30 June 2014 | 0.78 | 0.82 | 0.81 | 0.71 |

“Observed Values” | (2/3 h_{C}) and (1/8 h_{C}) | Raupach (1994) | Choudhury and Montheith (1988) | Massman (1997) | |
---|---|---|---|---|---|

d_{0} | Mean: 3.35 Std: 1.94 | 5.33 | 5 | Mean: 4.66 Std: 0.23 | Mean: 4.05 Std: 0.43 |

z_{0M} | Mean: 0.52 Std: 0.3 | 1 | 0.687 | Mean: 1.13 Std: 0.2967 | Mean: 1.24 Std: 0.06 |

**Table 4.**RMSD for Rn, G, H and LE from the application of TSEB and the different versions with T

_{RAD}derived from the four-way radiometer (ECT).

RMSD (W m^{−2}) | TSEB-G_{M} | TSEB-G_{R} | TSEB-M_{R} | TSEB-G_{GT} | TSEB-M_{GT} | TSEB-G_{M-PT} |
---|---|---|---|---|---|---|

Rn | 27 | 27 | 27.5 | 30 | 30 | 27 |

G | 28 | 28 | 28 | 28 | 27 | 28 |

H | 47 | 48 | 46 | 55 | 53 | 50 |

LE | 50 | 46 | 46 | 48 | 44 | 60 |

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**MDPI and ACS Style**

Andreu, A.; Kustas, W.P.; Polo, M.J.; Carrara, A.; González-Dugo, M.P. Modeling Surface Energy Fluxes over a Dehesa (Oak Savanna) Ecosystem Using a Thermal Based Two-Source Energy Balance Model (TSEB) I. *Remote Sens.* **2018**, *10*, 567.
https://doi.org/10.3390/rs10040567

**AMA Style**

Andreu A, Kustas WP, Polo MJ, Carrara A, González-Dugo MP. Modeling Surface Energy Fluxes over a Dehesa (Oak Savanna) Ecosystem Using a Thermal Based Two-Source Energy Balance Model (TSEB) I. *Remote Sensing*. 2018; 10(4):567.
https://doi.org/10.3390/rs10040567

**Chicago/Turabian Style**

Andreu, Ana, William P. Kustas, Maria Jose Polo, Arnaud Carrara, and Maria P. González-Dugo. 2018. "Modeling Surface Energy Fluxes over a Dehesa (Oak Savanna) Ecosystem Using a Thermal Based Two-Source Energy Balance Model (TSEB) I" *Remote Sensing* 10, no. 4: 567.
https://doi.org/10.3390/rs10040567