Land surface models, mathematical representations of surface-atmospheric exchanges, are important tools to understand fluxes of energy and mass, which drive climatic and Earth system processes [1
]. These models provide vital information to understand the response of ecosystems to climate and environmental changes, and monitor Earth system dynamics [2
]. Latent heat flux (LE), the aggregated water flux consisting of evaporation from the soil and other wet surfaces (LEs
) and plant transpiration (LEc
), has recently been the subject of extensive research [4
] due to its importance in evaluating ecosystem functional properties. It is a key process that interlinks the water and energy budget along with carbon cycling through the processes of transpiration and photosynthesis [5
]. However, LE is a complex and difficult to estimate phenomena, as it is affected by numerous variables related to the characteristics of the soil-surface, atmosphere and vegetation [6
]. As a result, LE is highly variable and dynamic, making remote sensing techniques notably useful to predict it at different temporal and spatial scales.
Different remote sensing methods have been proposed to estimate LE, which range from empirically-based to more process-based modeling schemes [7
]. Among these, surface energy balance (SEB) models estimate LE as the residual of the energy balance, which exploit radiometric land surface temperature (LST) from thermal remote sensing as a key boundary condition [10
]. There are two main types of SEB models: one-source models that do not discriminate between vegetation and soil components and dual-source models, which explicitly separate the temperature and energy exchange between the vegetation and soil sources considering the directional effects in the remotely sensed radiometric temperature. The two-source energy balance (TSEB) model [10
], has been applied in a variety of landscapes obtaining reliable estimates of LE [15
], including for water stressed conditions [21
]. TSEB was originally developed for homogeneous cover types, however, adaptations to the model framework have been implemented to better depict partial canopy cover [14
]. Past studies demonstrated that TSEB better accounted for the effects of partial vegetation cover compared to one-source models [15
]. However, in heterogeneous and complex surfaces such as tree-grass ecosystems (TGE), Earth observation and modeling methods tend to have greater uncertainties, e.g., [24
TGEs, a prevalent savanna-like landscape covering nearly 15% of the total Earth surface [26
], are frequently located in semi-arid regions with limited and highly seasonal water availability [27
], where a greater urgency is needed to monitor the scarce water resources. Since TSEB treats the vegetated layer as a unique layer, the parameterization and application of this model poses greater difficulty in a TGE landscape where two (sometimes three) distinct vegetation covers are present (i.e., isolated trees over a grassland and/or shrubland), making it difficult to represent the vegetation according to a unique set of parameters. Additionally, in these semi-arid ecosystems, the degree in which each type of vegetation (i.e., tree and grass) influence land-surface interactions changes throughout the year depending on their differentiated phenological stages [28
]. During the growing season, trees and the grass understory, along with underlying soil, all interact to contribute to the radiative transfer and turbulent exchanges [29
]. However, during the dry summer periods, the grass layer senesces due to meteorological and soil conditions (i.e., water availability, air temperature, vapor pressure deficit), converting the system into (nearly) bare, rather rough, soil with scattered trees, substantially changing land-atmospheric dynamics [30
]. As Andreu et al. [31
] discussed, further adaptations to the TSEB model structure and parameters may be necessary to accurately simulate energy fluxes over TGEs due to the multiple vegetation layers present. In this regard, remote sensing data and algorithms can play a pivotal role in improving land-surface modelling by fully exploiting information from different sensors (e.g., synthetic-aperture radar (SAR) and light-detection and ranging (LiDAR)) to better estimate auxiliary variables (e.g., canopy height) that are normally assumed or static. To account for these spatial and temporal complexities, TSEB was adapted here to consider two major phenological periods, based on when the grass layer is active during the growing season and not active (i.e., senesced) during the dry summer period.
Prior to adapting models, sensitivity analyses (SA) are a useful tool for quantifying and pinpointing the different sources of uncertainties within the modeling procedure [32
]. This is especially useful to extract the most important and influential parameters or inputs within the model. Different SA methods exist which are often distinguished between local and global techniques [34
]. Local methods compute the degree in which the model output changes due to a change in a single parameter, while keeping other parameters constant (i.e., 1st order). On the other hand, global methods evaluate the whole parameter space simultaneously and, thus, compute both the main effect (1st order) and the interactions between parameters (second and higher orders) to obtain the total parameter contribution (total order) to the overall variability in model output. Local SA techniques are usually deemed unsuitable for complex non-linear models since they neglect the often strong and significant parameter interactions [35
]. While other studies have investigated the sensitivity of specific parameters or inputs within TSEB (e.g., [23
]) or performed a SA to optimize TSEB (e.g., [19
]), a comprehensive SA for TSEB has not been discussed in the literature, especially for complex ecosystems, such as TGEs, where surface heterogeneity may potentially lead to increases in parameterization and complexities.
Therefore, the hypothesis of this work is whether a relatively simple adaptation to TSEB, by considering two distinct modeling periods throughout the year and avoiding additional parameters or changes to the basic model structure, is able to reproduce reliable estimations of turbulent energy fluxes for a spatially and temporally complex semi-arid TGE. To quantify the different sources of uncertainty, the Sobol global SA [40
] method was used on the main parameters within TSEB combined with a local SA of the two main remote sensing-based inputs: LST and leaf area index (LAI). The modified model results were evaluated against three independent eddy covariance (EC) systems and lysimeter measurements located within the experimental site [42
The proposed TSEB-2S vastly improved model performance in simulating LE and H compared to the default TSEB configuration (RMSD and bias of modelled H decreases from 82 and −45 W m−2 to 55 and −5 W m−2, respectively). The simple assumption of two separate phenological and modelling periods, one dominated by a grass-soil system and the other dominated by a tree-soil system, allowed for a two-layer model to accurately simulate turbulent energy fluxes in an essentially three (tree-grass-soil) layer ecosystem. TSEB assumes only one vegetated layer, being more or less photosynthetically active, over a non-photosynthetically active layer (i.e., bare soil or similar). Therefore, it becomes difficult to properly parameterize the model when numerous vegetation covers are simultaneously present. Additionally, as in the case of many TGEs, the influence of the grass understory changes throughout the year, where it becomes largely non-photosynthetically active (i.e., not transpiring) during the summer. Therefore, these vastly different seasonal conditions and characteristics were better captured using TSEB-2S, by assuming a ‘dominant’ vegetation cover for different phenological periods, compared to the default, single mixed vegetation, configuration of TSEB (TSEB-DF). The relatively simple and automatic separation of seasons from a MODIS-NDVI time series can easily be extrapolated to other TGEs or similar temporally dynamic sites, as these data are globally available. The results also demonstrate that large changes to the vegetated surface have a considerable influence on the surface energy balance. This confirms the importance of vegetation characteristics in controlling and mediating ecosystem level energy fluxes, where seasonal dynamics and phenology of vegetation are key considerations for land-atmospheric modelling. The findings presented here describe a relatively simple and general approach to account for changes in land-atmospheric exchanges due to phenology such as those occurring in semi-arid TGEs. In this regard, a similar strategy can be implemented in other global soil-vegetation-atmosphere-transfer (SVAT) or prognostic models to better accommodate seasonality for ecosystems with comparable characteristics.
The TSEB-2S model demonstrated robustness, being able to accurately simulate different intra-annual dynamics for various years (i.e., different phenological timings) and sites with differing surface conditions, in this case, derived from a nutrient fertilization experiment (Figure 9
). Results and the associated magnitudes of errors for all TSEB-2S model runs are similar to the error bounds found in other energy balance model studies (e.g., [14
]) and close to the typical uncertainty of surface turbulent flux measurement systems (i.e., ~50 W m−2
]). For instance, RMSD of LE between 62 and 70 W m−2
were achieved by Timmermans et al. [23
], who compared the use of TSEB against a one-source energy balance model for a sparsely vegetated grassland and rangeland. In the work of Boulet et al. [78
], different dual-source model schemes were tested and obtained an RMSD between 53 and 73 W m−2
for midday instantaneous LE for both irrigated and rainfed wheat fields. Therefore, the results presented here, are in line with past studies related to LE retrievals, with these considering much more homogeneous land cover types, which better fit the assumptions inherent in SEB models compared to the multiple and more structurally complex vegetation cover in TGEs. Andreu et al. [31
] applied various modified versions of TSEB, notably with different wind profiles and roughness schemes, in similarly complex TGEs and reported errors between 44 and 60 W m−2
for simulated LE. These are comparable to the error bounds presented here even though quite different approaches were used. In our study, the basic TSEB model structure was not modified, instead opting to alter the model parameterization depending on the phenological period using typical land cover characteristics (i.e., grasslands and evergreen broadleaved trees). As such, the findings here may complement the methods used by Andreu et al. [31
], who also reported the largest errors during the dry, summer period.
The global SA demonstrated that TSEB was most sensitive to
. This is largely due to
being a key input to estimate the Ω (Kustas and Norman [14
]), which in turn affects the radiation interception and partitioning between the mixed vegetated and soil surfaces. The estimation of Ω is mostly based on the transmission through the vegetated layer where
is used to obtain a local LAI (LAI/
) and as an important weighting factor for the gap fraction estimation (Section 2.2.1
). These results are largely in line with results from Li et al. [39
], who found that the Ω uncertainties had a large impact on flux outputs from TSEB. They tested incremental
values, between 0.1 and 1, that resulted in sharp H changes, particularly between higher
values, an indication of a high sensitivity for this parameter. The
was found to be more sensitive compared to
even though both parameters are part of the initial canopy transpiration estimate from the Priestly-Taylor formulation (Equation (7)). This is the case since
is merely used as a priori estimate for initializing the model and is gradually decreased when there are conditions of water stress, until the energy balance is achieved with realistic daytime fluxes using LST as a boundary condition (as previously discussed in [10
]). Figure A4
shows the daily average trend for the retrieved effective
with TSEB-2S at CT in 2015. Note in Figure A4
(defined for only the canopy source i.e., Kustas and Anderson [9
]) maintains closer to the initial value of 1.26 during the dry summer period since TSEB-2S is simulating the canopy transpiration as a scattered broadleaved evergreen tree cover, which has extensive root system able to withdraw water even under drought conditions. The b
coefficient, used to estimate the soil resistance to heat transport (i.e.,
), was the only more empirically derived parameter that demonstrated a relatively large influence on model results. However, no significant relationship (Figure A5
A, r = 0.01) was obtained between
and errors (i.e., residuals) in modelled H and a very small relationship between
(canopy boundary resistance) and errors in H was found (Figure A5
B, r = −0.19). The latter is likely caused by uncertainties in tree LAI, as
is inversely proportional to LAI since the canopy is considered as a set of single-leaf resistors placed in parallel.
The input SA showed that uncertainties in LST and LAI both translate into uncertainties in modeled H. However, model results were found to be much more sensitive to LST compared to LAI. Gan and Gao [38
] also found TSEB to be sensitive to biases in LST, where a 1K change is associated with median daily ~12–25 W m−2
bias. A local LAI SA in Li et al. [39
] added +-20% deviation to LAI and investigated the associated relative H change in TSEB. Their associated ~3–8% bias in modeled H is similar to the results presented here, with a 20% change in LAI being associated with a median H bias of 6.1% with TSEB-DF. As such, the more comprehensive SA analysis presented here, considering parameter interaction in the global SA combined with a local input SA, were largely in line with results presented in different local and parameter specific SAs from the literature. These results will be useful for future studies, as we quantified the relative influence of the different modeling components in TSEB, which may be similar for other thermal-based energy balance models.
This work additionally investigated the partitioning of LE, which is a complex process to separate in ecosystems that have multiple vegetation layers. As shown, bulk (soil + vegetation) fluxes were well modeled in TSEB-2S for different years and towers. However, the partitioning of LE had greater uncertainty, with biases observed comparing modeled LEs
to the lysimeter measurements (Figure 10
). Since total LE was well modeled, this indicates errors associated with the partitioning itself. This may be due to TSEB interpreting moderately stressed vegetation with a moist soil as fully transpiring vegetation with a dry soil. However, the partition of LE is largely controlled through LAI within TSEB [17
]. The poorer performance in the LE partitioning could be due to the assumed vegetation cover of the two different seasons not properly depicting the complex vegetation characteristics observed, affecting net radiation partitioning, notably during the growing season when the tree layer is neglected. TSEB’s relatively poor performance in partitioning LE was also observed over a vineyard in Kustas et al. [17
]. As stated in Kustas et al. [17
], more studies need to evaluate whether the poor partitioning is linked to uncertainties in input values (i.e., LAI) or biases caused by the modelling structure itself (i.e., initial potential canopy transpiration, radiation transfer).
As demonstrated, a simple adaptation to the modelling scheme in TSEB, depicting the phenological change in the vegetation source, were able to successfully simulate LE and H in a complex ecosystem. However, certain limitations are still present including the slight systematic underestimation of H during the grass growing season, particularly visible in the 2015 daily H time series (Figure 8
). This is likely due to the modeling scheme in this period ignoring the effect of the tree canopy layer on the turbulent transport and hence on the calculation of the aerodynamic resistances. Compared to grasslands, tree canopies are more aerodynamically coupled to the atmosphere and hence their aerodynamic resistance is lower, resulting in that trees can dissipate heat more efficiently [43
]. As discussed by El-Madany et al. [43
], tree canopies in the Majadas experimental site were an additional H source, even though they tend to have a lower LST than the grass layer. As such, ignoring the tree canopy during the growing periods may not adequately represent the turbulent transport characteristics of the ecosystem, resulting in H underestimations, in some cases. On the other hand, neglecting the tree canopy during the growing season was supported by the evidence that the understory layer dominates LE in this site (as shown by Perez-Priego [42
]). This may explain why TSEB-2S was largely capable to accurately model LE during this seasonal period for the different years assessed. Further adaptations to the TSEB model scheme may be needed for the more operational and larger scale use of this model, notably for similarly complex ecosystems such as TGEs. The differences between soil, grass, and tree layers should inherently be integrated within the modelling structure to robustly consider their different geometric, aerodynamic, and phenological properties and their resulting effect on energy fluxes.
When accounting for different phenological periods through an automatic vegetation seasonal change detection using a MODIS time series analysis, the TSEB model provided robust LE and H estimations for a three-layered heterogeneous and semi-arid TGE using a combination of satellite (LAI) and proximal (LST) sensors. This, in conjunction with the SA, confirms the important role that vegetation characteristics, notably its structure (i.e., ) and cover (i.e., and ), have on ecosystem level energy fluxes. The was the single most influential parameter on model performance, largely due to its role in characterizing vegetation clumping and how this, in turn, interacts significantly with other parameters. In addition, the uncertainties related to the traditionally remotely sensed derived inputs, notably LST, showed an important influence on output uncertainties.
The LE partitioning, between canopy and soil, showed a larger bias compared to the bulk fluxes. Based on this, further research should focus on the understanding of the radiation partitioning between the canopy and soil layers, and particularly, inherently accounting for the important differences between soil, grass, and tree layers of TGEs within the modeling structure. However, the relative simplicity of TSEB-2S has the potential to be applied with both satellite and/or airborne data over similarly complex landscapes in different regions. This may provide a simple solution to improve remote sensing-based flux products over semi-arid TGEs and other savanna-like ecosystems, which often assume a homogeneous vegetation layer.