A revised version of the surface energy balance system model known as SEBS (Su, 2002) was used to estimate land heat fluxes, integrating remote-sensing and meteorological forcing data. A brief description of the model is presented below (for further discussion, see Su, 2002, and Chen et al., 2013). The latent heat flux (LE) was computed as a residual of the surface energy balance equation: 1LE=Rn-G-H, where Rn is the net radiation, G is the soil heat flux and H is the turbulent sensible heat flux. The net radiation is calculated using the following equation: 2Rn=1-αSWd+εLWd-εσLST4, where α is broadband albedo, SWd the downward shortwave radiation, LWd the downward longwave radiation, ε the land surface emissivity, σ the Stefan–Boltzmann constant and LST the land surface temperature.

The soil heat flux is derived from its ratio to the net radiation (Γ) using Eq. (3): 3G=RnΓc+1-fcΓS-Γc. This ratio is assumed to be equal to 0.05 (Monteith, 1973) for surfaces with fully covered vegetation (Γc) and 0.315 for bare soils (Γs) (Kustas and Daughtry, 1990). The green canopy cover, fc, is determined using the normalized difference vegetation index (NDVI) in Eq. (7).

Using Eqs. (1) to (3) and energy balance considerations for limiting cases, the following reductions can be applied: (i) under the dry limit (Eq. 4), the evapotranspiration, λEdry, is assumed to become zero due to the limitation of soil moisture and the sensible heat flux, Hdry, is at its maximum, 4λEdry=Rn-G-Hdry≡0. (ii) Under the wet limit (Eqs. 5 and 6), the evaporation takes place at a potential rate, λEwet, only limited by the available energy at the given surface and atmospheric conditions. The sensible heat takes its minimum value, Hwet, with the internal resistance of the Penman–Monteith combination equation in the form written by Menenti (1984), ri≡0, by definition. 5λEwet=Rn-G-Hwet6Hwet=Rn-G-ρCprew×es-eγ/1+Δγ, where ρ is the density of air, Cp the specific heat at constant pressure, e and es the actual and saturation vapor pressure respectively, γ the psychrometric constant, Δ the rate of change of saturation vapor pressure with temperature and rew the external or aerodynamic resistance. The sensible heat is computed according to the Monin–Obukhov similarity theory and limited by the dry and wet conditions. A complete description of the model and the use of the dry and wet limits can be found in Su (2002).

For the application of SEBS over the dehesa area, two surface variables, fc and the height of the canopy (hc), have been adapted to the specific characteristics of this ecosystem. The green canopy cover (fc) and leaf area index (L) were calculated using the following equations (adapted from Choudhury et al., 1994): 7fc=1-NDVImax-NDVINDVImax-NDVImin1ξ8L=-1kln⁡1-fc, where NDVImax and NDVImin represent a surface fully covered by vegetation (∼ 0.94) and completely bare (∼ 0.15), respectively. The parameter ξ represents the ratio of the canopy extinction coefficient (K′) to a leaf angle distribution term (k). k was assumed to be equal to 0.5 for a random distribution of leaves, as the ecosystem contains erectophile grasses and planophile oak tree leaves (Andreu et al., 2019). K′ adopted a value of 0.8 obtained from experimental data and within the range proposed for NDVI by Baret and Guyot (1991). NDVI data were provided by the MODIS instrument, averaging the 16 d original product to a monthly scale.

The height of the canopy was computed to account for variations in the tree component. This variable is needed for calculating the momentum roughness length and, thus, important for the sensible heat calculation. The tree stratum of the dehesa is quite homogeneous in composition, dominated by mature Quercus ilex sp., and the grassland canopy has a very high variability of low-height herbaceous species. Considering these reasons, the ecosystem structure has been simplified to compute hc in the following way: a constant height of 8 m has been assigned to oak trees, which is multiplied by its ground coverage in each pixel. Oak fc is computed annually using summer NDVI in Eq. (7). During the summer, the grasslands are dry, and the only photosynthetically active vegetation contributing to the NDVI signal is the oak trees. The grassland height is low (< 1 m), affecting the effective canopy height of each pixel less than the trees, and it is also difficult to compute based on monthly vegetation indices given the high species variability. For this reason, the grassland height has been discarded, and only the contribution of trees was considered to compute hc. Thus, a single hc value was used for every month of a year. This simplification of a complex system certainly may contribute to the error of modeled fluxes. However, it was an operative solution considering the scale of this study.

The SEBS model was originally designed for instantaneous applications. Monthly calculations using the same model were demonstrated by Chen et al. (2014). The structure of the model was not changed, and the implementation differed in the input datasets. The model was applied over the entire Iberian Peninsula with a spatial resolution of 0.05∘ and a monthly input dataset. Satellite and meteorological input datasets are described in Table 1. All datasets were spatially averaged or subdivided to a common resolution of 0.05∘.

The land surface temperature (LST) was provided by the MODIS instrument, using the monthly mean of the day and night LST product, which provides the most complete coverage. The accuracy of this product, a key variable in SEBMs, was evaluated by Chen et al. (2017), supporting its applicability for climate studies and numerical model evaluation.

Meteorological data were provided by the ERA-Interim, a global atmospheric reanalysis dataset from the European Centre for Medium-Range Weather Forecasts (ECMWF). Monthly means of daily means were produced by ECMWF as the average of the four main synoptic monthly means at 00:00, 06:00, 12:00 and 18:00 UTC. The forecast model, data assimilation method and input datasets used to produce ERA-Interim can be found in Dee et al. (2011) and a description of the product archive in Berrisford et al. (2011).

To analyze model results, the monthly rainfall gridded data of the Climatic Research Unit (CRU) Time-Series (TS) Version 3.21 (Harris et al., 2014), provided by the Global Climate Monitor System (Camarillo-Naranjo et al., 2019), have been averaged over the dehesa area of the Iberian Peninsula.

Two experimental sites (Fig. 1) with similar flux measurement instrumentation have been used to validate the evapotranspiration and other energy fluxes estimated using the SEBS model. Both eddy covariance towers, named Sta.Clo (Santa Clotilde, Andalusia; 38∘12′ N, 4∘17′ W; 736 m a.s.l.) and ES-LMa (Boyal de Majadas del Tiétar, Extremadura; 39∘56′ N, 5∘46′ W; 260 m a.s.l.) are located over dehesa-type ecosystems under similar management and a landscape of scattered oak trees with a fractional cover of around 20 %, in southern and southwestern Spain, respectively. The convective fluxes of the systems are measured above the tree height (at 17 m in Sta.Clo and 15 m in ES-LMa), with closure balance errors of 20 % and 14 %, both values being within the range found by other authors (Foken, 2008; Franssen et al., 2010). For ES_LMa the processing of the data corresponded to the procedure standardized by the FLUXNET network (https://fluxnet.org/, last access: 5 February 2021). For Sta.Clo, detailed information on the measurements and the processing of the data can be found in Andreu et al. (2018a, b). In this case, the comparison period was selected attending to the quality of the data, and some months (3 of 36) were discarded due to missing information. Soil moisture, precipitation and other complementary measurements of the vegetation (reflectance, L, green canopy cover) were used to characterize the dynamics of the vegetation and the soil water status throughout the year.

The area contributing most to the fluxes measured was estimated by using Schuepp et al. (1990) and varied between 1 and 2 km. These footprints are lower than the pixel size of 5 km used for the application of the SEBS model. However, the homogeneity of the system, with similar tree ground cover fraction and pasture management at several kilometers around the towers, supported the capacity of these sites to serve as a reference for the validation of modeled fluxes. In both cases, the good correspondence between the model input meteorological data at the tower's location and the ground measurements was verified (data not shown).

Monthly rainfall data for the 17 years of the study were provided by the closest weather station to each site, located 3 and 16 km from Sta.Clo and ES-LMa towers, respectively. Both of them are operated by the Spanish Meteorology Agency (AEMET).

Model performance was quantified via the root mean square difference (RMSD) and the coefficient of determination (R2) between the modeled and observed fluxes. In addition, the mean bias error (MBE), computed by taking the difference between predicted and observed fluxes, was used to assess model under- and overestimations.

The relative evapotranspiration is the ratio of actual to potential or reference ET (ET / ETo). It has been used as an indicator of crop water stress (Anderson et al., 2015, 2016), of drought (Anderson et al., 2011) and as a proxy for soil moisture (Su et al., 2003). The same approach is used worldwide in irrigation engineering to compute crop water requirements following FAO (24 and 56) guidelines (Doorenbos and Pruitt, 1977; Allen et al., 1998). The reason for normalizing ET by ETo is to separate the ET signal component responding to soil moisture from variations due to the available energy. Anderson et al. (2011) showed that anomalies in ET / ETo were more strongly correlated with other drought indices as were anomalies in ET for most US climatic divisions, showing strong agreements in the southwest of the country, with a similar climate to the study area. The comparison of both variables anomalies has also been performed here.

Anomalous water stress conditions indicating drought were assessed here with the standardized values of relative ET. FAO56 reference ET (Allen et al., 1998) was selected to estimate the atmospheric evaporative demand (AED), given the difficulties of reproducing the biological control of the transpiration, even at potential rates, of the different types of vegetation conforming this ecosystem.

The vegetation water stress caused by the long dry summers of the Mediterranean climate can be considered to be the “normal” state of the system for several months of the year. To identify unusually dry conditions indicating drought, standard (z) scores of this variable (ET / ETo) for a given month/year have been computed. This standardization procedure assumes that the data follow a normal distribution. Some authors (Sheffield et al., 2004; Cammalleri et al., 2015) have pointed out that soil moisture and the water deficit index derived from it are generally characterized by a skewed distribution and can be statistically better represented using the beta distribution. In this case, the analysis of ET and relative ET monthly histograms (shown in the Supplement) indicated that most months presented an approximately symmetric distribution, with skewness between -0.5 and 0.5 for both variables. Among the months studied, 3 months were moderately skewed, and only 1 month (for ET) and 2 months (for ET / ETo) were slightly above 1, backing up the use of z scores for the standardization of this variable. Annual drought analyses were performed by averaging monthly anomalies.

Drought intensity is defined here in terms of the maximum negative anomaly of relative ET values reached during an event (thus using the standard deviation as a measure of its departure from the mean) and the drought event duration as the successive number of months with negative anomalies. To classify the events occurred during the study period, the following thresholds have been used: severe drought (anomalies <=-1.5); moderate drought (anomalies between -1 and -1.5) and mild drought (anomalies between -1 and 0). These classes are used for both annual and monthly time steps.

Two variables, vegetation coverage (fc) and rain-fed wheat production, have been selected as drought impact indicators. The vegetation condition and the failure of crops are known consequences of a declining soil moisture, and both have been used previously as indicators of drought (Liu and Kogan, 1996; FAO, 1983). Winter cereals are the main cropping system of these areas, in which the low fertility of the soils does not allow for a more intense agricultural use. Its growth cycle is similar to that of the natural grasslands, with both of them escaping drought and coping with the long summer dry season by completing their life cycle before serious soil and plant water deficits develop. Given that no irrigation is provided, the impact of moisture deficits over its yield can be consider an indirect indicator of the impact of drought on dehesa herbaceous vegetation. Annual yield statistics (http://www.mapama.gob.es/es/estadistica/temas/estadisticas-agrarias/agricultura/esyrce/, last access: 5 February 2021) have been gathered and aggregated for the dehesa area (Fig. 1).

The comparison of SEBS model estimation of monthly energy fluxes with measurements at the two eddy covariance (EC) towers during a total of 6 years, 2009 to 2011 for ES-LMa and 2015 to 2017 for Sta.Clo, displayed in Fig. 2, generally showed good agreement, with an average root mean square difference (RMSD) of 21 W m-2 and R2 of 0.76, for all energy fluxes and both sites. The estimations of the convective fluxes (LE and H) show higher deviations, with RMSD = 26 W m-2 on average, than Rn and G, with RMSD = 15 W m-2. Model performance at ES-LMa site was, in general, superior to that at Sta.Clo, with all the statistics metrics computed for the comparison (RMSD, MBE and R2) presenting lesser dispersion and slightly lower errors. LE was slightly overestimated at both sites (MBE = 10.3 and 2.8 W m-2 at Sta.Clo and ES-LMa, respectively), which is in agreement with previous applications of the model (Michel et al., 2016). This overestimation was particularly significant for some springtime months at Sta.Clo, when the sensible heat was underestimated by the SEBS model (Chen et al., 2019). It is worth noting than the model forces the closure of the energy balance, and the error in LE can be attributed to the propagation of errors in all the other balance components. However, LE estimations presented a similar or lower RMSD than other applications of the SEBS model (Chen et al., 2014; Vinukollu et al., 2011). In particular, the work by Chen et al. (2014) estimated energy fluxes over China at the same temporal scale and with similar input databases. The comparison with measurements at 11 Chinese flux towers presented results that were very close to the ones obtained by this application. Mean RMSDs for all fluxes were alike (RMSD = 22 W m-2 was reported by Chen et al., 2014), with a marginally better performance for convective fluxes and a poorer one for Rn and G (RMSDs in China were 22 and 24 W m-2 for convective fluxes and, Rn and G, respectively).

Figure 3 presents the evolution of modeled ET and ETo, ET / ETo and measured precipitation from 2001 to 2018, aggregating the hydrological year (between 1 October and 30 September) at the two experimental sites. It can be observed that annual ET variations for the period followed a similar pattern of precipitation at both sites, confirming the predominant control of water availability over the evaporation in these systems. This control is consequently extended to ecosystem productivity, and in most years the water consumption, coupled to biomass production, is close to the total rainfall. Tree density is similar at both sites, and the differences in water consumption between them are explained by variations in annual pasture production, due to differences in water availability and soil properties. Very wet years, and those with average rainfall but intense precipitation events producing an increase in runoff, did not follow this pattern. This can be observed by the runoff recorded at Sta.Clo watershed reservoir (Fig. 3a). The main land use of this small watershed (48.4 km2) is dehesa, but other uses can be found as well, such as olive orchards and field crops.

Annual runoff measurements followed a close relationship (data shown in the Supplement, Fig. S2) with the annual aridity index (Budyko, 1974) estimated at Sta.Clo following Arora (2002) as the ratio between potential evaporation and annual precipitation. On average, we found aridity indices of above 1 at both sites, indicating dry regions where the evaporative demand cannot be met by precipitation. In this case, AED was computed using Penman–Monteith for comparison purposes. Sta.Clo site is noticeably less arid than ES-LMa, with an aridity index equal to 2.9 and 3.75 on average for the 17 hydrological years at Sta.Clo and ES-LMa, respectively, with both of them falling under the category of a semi-arid climate regime (Ponce et al., 2000). The two sites presented similar annual ETo values for the period (Fig. 3), but annual precipitation was around 200 mm higher, on average, at Sta.Clo, with a higher and more variable ET / ETo throughout the years. What can also be observed in Fig. 3 is the complementary relationship between actual and reference evapotranspiration at this temporal scale, with the sum of annual ET and ETo approaching a constant value at both sites, confirming the complementary hypothesis (Bouchet, 1963; Morton, 1975; Brutsaert and Stricker, 1979).

Drought was characterized on an annual scale over the experimental sites and the whole area of the dehesa of the Iberian Peninsula using the relative evaporation anomalies. Figure 4 presents their evolution for the two sites throughout the study period. A clear similarity can be observed in the main negative anomalies, which identify the most severe droughts during the years 2004/2005 and 2011/2012 at both sites, despite the differences in aridity and the distance (Fig. 1) between them, indicating the extended area and intensity of both events. Differences are more evident in the case of the mild droughts, occurring at both sites but with different intensities during two periods, 2007 to 2009 and 2016 to 2018.

When the whole dehesa area is considered (Figs. 5 and 6), a more complete view of the general intensity, impact and spatial distribution of those dry periods can be obtained. Figure 5 aggregates, for the total dehesa area, the evolution of the relative ET anomalies, together with the exchanges of energy between the surface and the atmosphere, the green canopy cover and the production of rainfed wheat. The last two variables were selected as indicators of the impact of water scarcity on the system.

The 2 severely dry years identified at the experimental sites were the driest ones for the entire dehesa area, with 2004/2005 standing out as the most severe event of the time series. None of them lasted more than 1 year. For these 2 dry years, a reduction in the latent heat can be observed when compared to the complete series, producing a swap with the sensible heat in the second position in magnitude of the energy balance components. A rise in the surface temperature, increasing the difference with the air temperature, is also observed for those dry years. The order of severity in dryness, established by the magnitude of negative values of ET / ETo anomalies, is also observed in their impacts over the system (Fig. 6). In 2004/2005, the wheat production in the area was reduced by almost half of the average (45 %) for the period analyzed, and the vegetation groundcover fraction fell by 20 % compared to the average of the same period. This severe drought affected the entire Iberian Peninsula, with Spanish and Portuguese cereal and hydroelectricity production decreasing by 40 % and 60 % with respect to the average (Garcia-Herrera et al., 2007) and a 10 % reduction in total EU cereal yields (UNEP, 2006). The event during 2011/2012 was among the largest and most severe ones in Europe for the 18-year simulation period analyzed by Cammalleri et al. (2015), contributing to a global decline in grain production.

Figure 6 shows maps of ET / ETo anomalies in Iberia for the 17 years of the study, highlighting the dehesa area of interest in this work. The spatial variability of these anomalies for most years is significant, although prevalently dry and wet years can be distinguished. In 2004/2005 and 2011/2012, the drought was severe and affected most of the area of interest, as the aggregated values of Fig. 5 also point out. In 2008/2009, the water stress was milder in the western area, as can be observed in Fig. 6, than at the experimental site of Sta.Clo (Fig. 4) located in this part of the region. The recovery of the vegetation water status, in most areas, was achieved the year following dry ones.

The monthly evolution of relative evapotranspiration anomalies is displayed in Fig. 7a, with negative values indicating water stress conditions highlighted in red. Absolute ET and ETo values, used to calculate these anomalies, are shown in Fig. 7b together with monthly rainfall for the period. One can observe the alternation of complementary and parallel characteristics of ET and ETo throughout the year. The longest complementary period indicating water-limited ET conditions, starting in May for most of the years, is confirmed by the decreasing trend in rainfall starting in that month. At the end of the summer when the first rains arrive, the trend of ET and ETo changes, producing a secondary peak in ET, much weaker than the one earlier in the year, that lasts until the energy-limited parallel phase starts in November. Both variables follow a concurrent rise from January until the soil water deficit limits ET again.

The annual fluctuations of the green canopy cover (thick green line in Fig. 7a) followed the expected seasonality of Mediterranean vegetation, corresponding to the dynamics of ET and ETo changes. The maximum coverage (March and April) corresponds to the peak of grassland production (and ET although with different shape), and the minimum appears during the dry summer, only endured by the oak trees. In some years, the growing season presents a bimodal shape, with an initial peak produced by autumn pastures, which is also reflected in ET values. It can be observed mostly in wet years (e.g., 2003, 2007, 2011), with the vegetation growth following a pattern that can be related to the soil water availability, represented here by the ET / ETo anomalies.

The duration and intensity of each drought event help to explain the response of the vegetation during these periods. In this sense, the two main drought events identified on an annual scale (2004/2005 and 2011/2012) presented drier than normal conditions during the whole or most of the year. The first event was longer (16 months in the first case, prolonging the drought to the beginning of the following year) and with higher negative values than the second one, of an 11-month duration, explaining the greater impacts detected on the vegetation and cereal yield. Other dry periods, in 2009, 2017 and 2018, presented consecutive negative anomalies for 10 to 11 months, but, in some cases, the non-homogeneous distribution of the drought, observed in Fig. 6, may have undermined the impact analysis on this aggregated spatial scale. In terms of impact assessment, the time of the year with peak negative anomalies is important, with springtime events producing greater impacts (e.g. in 2004/2005 the highest negative values corresponded to January, February, April and May 2005).

During the dry years, the annual vegetation growth pattern varies with respect to the typical one, depending on the duration and severity of drought events. The dynamics of the vegetation in this system allows for a separate analysis of the effect of water scarcity over trees and pastures. The dashed green lines (Fig. 7a) show the changes in annual maximum and minimum values of fc, with the maximum ones mostly expressing the impact on pasture, and the changes in the minimum ones representing only the impact over the tree canopy. The decreases in pasture fc are more pronounced than changes in oaks fc, as grasslands are more abundant, and their roots are mostly located in the first centimeters of soil. On the contrary, the rooting system of the oak tree is in fact adapted to the regular dry periods of the Mediterranean climate, exploring a large volume of soil that can reach maximum values of around 5 m in depth and 30 m in horizontal extension (Moreno et al., 2005). The small decreases, observed in oaks fc in Fig. 7a during dry years, generally recovered within 1 or 2 years. This response of the tree leaf area is associated with low-frequency oscillations, such as annual rainfall (Poole and Milles, 1981). This is also supported by the variance observed in fc that can be explained by the anomalies of relative evapotranspiration of previous months. During the spring, the highest correlation coefficients are obtained for the previous 2 or 3 months (e.g., average fc for the peak month, April, is correlated with average anomalies from February to April with an R2 equal to 0.76 and with anomalies of the previous year with an R2=0.52). However, during the summer, the coverage of the vegetation can be better explained by what has happened during the previous year (e.g., R2 is equal to 0.39 for average August fc and the anomalies of the two previous months and 0.64 for the anomalies of the year), suggesting that those values of fc might be linked to processes occurring at different timescales.

A more detailed analysis is required, but these results support the conclusion that the drought events characterized for this period did not cause any permanent damage to the vegetation, considering both the grasslands and the oak trees.

Similar results can be derived from the analysis of ET anomalies. Figure 8 presents a comparison of monthly anomalies of ET, ET / ETo and fc. The anomalies of ET and ET / ETo showed a high similarity for the conditions of the study, with correlations of R2=0.76 at monthly scale and R2=0.82 at seasonal scale (results presented in Figs. S3 and S4). It suggests that ET anomalies could be an option to monitor drought in dehesa areas. Nevertheless, the computation of ETo does not require additional variables than those already used by the energy balance models, with quite a straightforward computation. Once actual ET is estimated, the computation of ET / ETo takes very little effort and adds some confidence to the focus on the soil moisture signal. Regarding the evaluation of fc anomalies, it can be derived that the drought events identified using this variable would have been the same as using ET or ET / ETo but with different intensities and duration. The main differences can be found during the cold winter months when the vegetation is largely dormant. In these cases, the anomalies of fc, similar to the performance of other indices based on vegetation, such as the Vegetation Condition Index (VCI; Heim, 2002) have a limited utility. The results are more comparable and could be more useful during the growing season.