Evaporative Fraction as an Indicator of Moisture Condition and Water Stress Status in Semi-Arid Rangeland Ecosystems

Rangeland monitoring services require the capability to investigate vegetation condition and to assess biomass production, especially in areas where local livelihood depends on rangeland status. Remote sensing solutions are strongly recommended, where the systematic acquisition of field data is not feasible and does not guarantee properly describing the spatio-temporal dynamics of wide areas. Recent research on semi-arid rangelands has focused its attention on the evaporative fraction (EF), a key factor to estimate evapotranspiration (ET) in the energy balance (EB) algorithm. EF is strongly linked to the vegetation water status, and works conducted on eddy covariance towers used this parameter to increase the performances of satellite-based biomass estimation. In this work, a method to estimate EF from MODIS products, originally developed for evapotranspiration estimation, is tested and evaluated. Results show that the EF estimation from low spatial resolution over wide semi-arid area is feasible. Estimated EF resulted in being well correlated to field ET measurements, and the spatial patterns of EF maps are in agreement with the well-known climatic and landscape Sahelian features. The preliminary test on rangeland biomass production shows that satellite-retrieved EF as a water availability factor significantly increased the capacity of a remote sensing operational product to detect the variability of the field biomass measurements. OPEN ACCESS Remote Sens. 2014, 6 6301


Introduction
The ecosystem carrying capacity and food security of the West African Sahel relies on annual vegetation production, which is concentrated in a short rainy period of four months, on average, between July to October [1]. The majority of the Sahelian livelihood counts on these wet months to get by in the dry season. The management of existing natural resources by the local population has developed several strategies to cope with climatic difficulties, such as exploiting herd transhumance at the beginning of the dry season [2] or handling the seedling date in the beginning of the rainy period [3].
However, recurrent erratic rainfall or a drought period could affect Sahelian food security, as happened during the great drought of the past century [4] and recent local food crises [5]. Despite several adaptations of the Sahelian population to erratic climate conditions [6], food security still remains a concern, and an accurate estimation of regional yields plays an important role in food security [7].
The awareness of rangeland production in relation to water availability is of major interest for the implementation of operational monitoring systems to support policies aiming at reducing the socio-economic impacts of environmental stresses. As water availability is the main limiting factor for vegetation production, especially where average annual rainfall is lower than 500/600 mm [8,9], the interest to estimate rainfall and soil moisture at the regional scale in relation with biomass production has earned a lot of attention.
Several recent studies analyzed time series of rainfall and vegetation indices highlighting the Sahel as an area where vegetation production is rainfall driven and only locally influenced by human activities [9][10][11][12][13]. Other works in the area compared vegetation production to trends of soil moisture [14] and rain use efficiency [15], identifying water availability as the main driver of vegetation growth and dynamics in the Sahel. A shortwave infrared water stress index (SIWSI) has been proposed as an indicator of vegetation water stress [16], while a combination of thermal data and vegetation index [16] were used to produce qualitative maps of soil moisture along the Senegal River.
Compared to these methods, the estimation of evapotranspiration (ET) at the regional scale could give a more quantitative assessment of vegetation water status. ET is a key component of the water budget, and its estimation at different scales is of outmost importance for water management in agriculture [17] and food security programs [18]. ET can be appropriately measured at the field scale by lysimeters, scintillometers or eddy correlation techniques [18]. However, being highly dynamic in space and time because of complex interactions between soil, vegetation and climate [19], the quantification of its flux at the watershed scale is much more difficult than at a specific site [20].
Traditional methods to estimate ET assume homogeneous vegetation cover and structure, but these conditions are hard to meet for large regions [21]. For studies at regional and continental scales, monitoring models are coupled with remotely sensed data that can cope with the spatial and temporal variability of surface characteristics that affect evapotranspiration processes [18]. Several surface from MODIS products; (ii) to evaluate EF estimation using in situ data and to assess EF maps at the regional scale; and (iii) to evaluate the improvement brought by satellite-retrieved EF to the accuracy of the biomass production model.

Study Area
The study area covers 1200 × 2400 km over Niger and Chad. The northern part includes the Sahara Desert, where less than 200 mm of rain falls every year and human presence is almost absent (Figure 1). The central part is located on the Sahelian belt, identified by the isohyets of 200 and 600 mm. This zone is mainly characterized by semi-arid savannah, where pastoralism is the most important livelihood activity, with localized evidence of agricultural activity (<20% of cultivated areas; [48]). The southern part of study area belongs to the Sudanian savannah, characterized by wetter climate (annual rain greater than 600 mm), an intensive farming system and less dependency on rain for vegetation productivity [4,10]. The rainy season of the whole study area is essentially from July to October and slightly longer in southern areas, with almost zero precipitation during the rest of the year.
A number of humanitarian crises have hit this area over recent years; although several are from concurring causes, such as food supply, livestock management, environmental degradation and household coping capabilities, low or erratic rainfall remains the key factor triggering the crisis [4,5,49]. In this region, the population has increased during the past 25 years [50]. The rural population is still growing, contrary to many other parts of the world, leading to heavy pressure on the environment, especially during adverse years. The study area overlaid on the regional GlobCover (GC) map of Africa [51]; the red star shows the position of the eddy covariance station; the red diamonds represent the field sites; the blue lines indicate the isohyet boundaries of 200-600 mm/year.

Earth Observation Data
According to the S-SEBI approach [43], the retrieval of EF from satellite data is based on the relationship between albedo and land surface temperature (LST). Two MODIS products were then considered: MCD43B3, i.e., the hemispherical reflectance (black-sky albedo) 8 days at 1-km spatial

Site1 Site2
Site3 resolution, and MOD11A2, i.e., land surface temperature 8 days at 1-km spatial resolution [52]. In order to cover the entire area of interest, two MODIS tiles (h18v07, h19v07) were downloaded for 10 years (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009), summing up to about 450 images per tile. Other satellite-derived products were used for analysis and evaluation purposes. For the analysis of the EF contribution to biomass production, we used dry matter productivity (DMP) maps [53]. DMP is a satellite-derived product, developed at the Flemish Institute for Technological Research (VITO), that quantifies the daily increase of dry biomass (growth rate) and is expressed as kilograms of dry matter (kg•DM) per hectare per day. The DMP product used in this exercise is a 10-day composite at 1-km spatial resolution covering the period 2000-2009.
Ancillary satellite data consist of rainfall and vegetation maps for the study area. Rainfall estimation (RFE 2.0) is provided by Famine Early Warning Systems Network (FEWS) every 10 days at 8-km spatial resolution [54]. RFE 2.0 is produced by a combination of Meteosat 5 data (satellite infrared data) and daily rain gauge data extracted from the WMO's Global Telecommunication System (GTS) with the additional integration of the two new Special Sensor Microwave/Imager (SSM/I) instruments on-board the Defense Meteorological Satellite Program satellites and the Advanced Microwave Sounding Unit (AMSU). Vegetation maps are represented by Normalized Difference Vegetation Index (NDVI ) provided by the SPOT-Vegetation satellite (VGT) sensor every 10-days at 1-km spatial resolution [55]. Finally for the analysis of EF behavior for different vegetation types, the regional GlobCover (GC) map for Africa with 300-m spatial resolution was used [51], which describes land cover classes over the entire study area.

Field Biomass and Flux Measurements
Field biomass data have been provided by Action Against Hunger (ACF) for three different sites in Niger ( Figure 1). Three site were analyzed: the first site is located in a tiger bush area 35 km north of Nigeria border (Site 1, Longitude 10.9, Latitude 13.7); the eastern site is located around Lake Chad (Site 2, Longitude 12.8, Latitude 13.95), while the northern site (Site 3, Longitude 6.8, Latitude 15.8) is located around Agadez, which is the upper limit of pasture activities [56,57]. Biomass measurements were collected following the quick double-sampling technique [58] to calibrate/validate ACF satellite maps of available forage [59]. Overall, 19 annual biomass values/data are available for the period of 2000-2009 (Table 1). These ground samples provide crucial information for the evaluation of EF capability as a water stress factor in biomass estimation. Flux measurements were collected at an eddy covariance tower situated in the Wankama catchment ( Figure 1), 60 km east of Niamey, Niger. This site presents the typical Sahelian landscape with sparse savannah and millet fields. Daily data of net radiation (W•m −1 ) was measured every minute by the tower instruments at a height of 2.5 m; these data are supplied to the user from the CarboAfrica project through FLUXNET measurement network as the average over 30-min periods [60]. This variable is available as a Level 2 product, i.e., not gap-filled, but checked/filtered for out-of-range values or clearly wrong data [60]. The daily latent heat flux data (W•m −1 ), processed with despiking, double rotation and gap filling following the indications of [61], were obtained from the publication of [62].

Estimation of Evaporative Fraction
The more widely applied method for ET estimation with passive remote sensing is the energy balance equation [18]. The land surface energy balance is the thermo-dynamic equilibrium between turbulent transport processes in the atmosphere and laminar processes in the sub-surface [17]. The basic formulation can be written as: where Rn is the net radiation, λE is the latent heat flux (λ is the latent heat of vaporization of water and E is evapotranspiration), G 0 is the soil heat flux and H is the sensible heat flux. Evaporation and transpiration occur simultaneously, and there is no easy way of distinguishing between the two processes: when the crop is small, water is predominately lost by soil evaporation, but once the vegetation completely covers the soil, leaf transpiration becomes the main process [28]. Many satellite-based approaches estimate daily ET, exploiting the EF factor [26,32,44], defined as the ratio between the latent heat flux (λE) and the available energy at the land surface (R n − G 0 ): In the present work, the EF estimation is obtained using the albedo-temperature method [43]. This approach allows one to compute the EF for every pixel as the relative distance from two lines, called the dry edge and wet edge, defined through a date-specific albedo-LST relationship ( Figure 2). The method's accuracy is dependent on the presence of humid and arid surfaces in the study area. Figure 3 provides the flow chart of the steps followed for the EF estimation from satellite products, for each available date of satellite products. Albedo and LST data were extracted from the digital numbers (DN) of MCD43B3 (layer 10) and MOD11A2 (layer 1), as indicated by the MODIS product description [52], while information on LST data quality as derived from Layer 2 of the MOD11A2.
Before starting the EF calculation, pixels flagged as -no-data‖ or -low quality‖ were masked out and excluded from the analysis.
To perform the EF estimation, the albedo-LST scatterplot is derived for a single date ( Figure 2) and analyzed to extract minimum and maximum temperature values for all of the albedo classes identified from statistical analysis [63].

Figure 2.
Scatterplot between surface albedo and LST. Blue circles correspond to minimum temperature values for each albedo class, which are used to compute the wet edge (lower limit of the graph) through linear regression. Red circles correspond to the maximum temperature values for each albedo class, which are used to compute the dry edge (upper limit) through linear regression. T H (maximum temperature) and T λE (minimum temperature) represent the values used in the calculation of the EF for the pixel i. The series of maximum and minimum LST values are used to calculate the date-specific dry and wet edge equation through linear regression: where m and q represent the parameters (slope and intercept) of the two regression lines, α 0 represents the albedo, while T is the land surface temperature. The dry edge was defined considering only pixels in the radiative controlled condition, commonly identified as the maximum temperature data for all of the albedo values greater than the inflection  [17]. This condition was empirically defined for an albedo value above 0.2, as used also by [44].
Exploiting the dry and wet edge, the EF can be calculated for every pixels i, dividing the difference between T H and the temperature pixel T S by the difference between T H and T λE : where T si is the temperature value of the pixel i and T Hi and T λEi are respectively the maximum and minimum temperature value derived by the dry and wet edge functions for a given albedo value α i . The EF equation can be rewritten as: this procedure, implemented with an ad hoc code in IDL language (Interactive Data Language, version 8.2), was applied to each pixel of the image and on each date available for both MODIS tiles h18v07 and h19v07.
The maps estimated at the same dates were mosaicked, obtaining EF maps of 122 × 2400 km to cover the entire study area.

Evaluation of the Estimated EF
Since it is well known that EF is related to water availability provided by rainfall, particularly in the natural vegetation of semi-arid environments, vegetation growth and land cover [29,35,38,64], we used the RFE, SPOT-VGT NDVI and GlobCover classes to assess the consistency of EF estimation. In particular, average and relative standard deviation (RSD) maps of EF are computed from the 448 8-day EF maps and analyzed for the major land cover classes of the study area, thanks to GlobCover map. This analysis was conducted in order to evaluate the coherence between the EF and the expected behavior over different vegetation covers.
In correspondence with the eddy covariance tower, EF behavior was compared to rainfall events and vegetation growth.
Quantitative evaluation of the reliability of EF estimations as a moisture (water stress) indicator is accomplished using the eddy covariance data from Wankama station.
Due to the different time steps of satellite estimation and flux measurements, the satellite-derived EF was compared with the 8-day average of daily ET corresponding to the MODIS composite. Data from the tower measurements identified as outliers from statistical analysis and EF satellite estimation flagged as low quality were excluded by the analysis. Moreover, thanks to Equation (7), it was possible to compare in situ estimation of EF with satellite-derived EF: where Rn d and λE d are the daily net radiation and the daily latent heat flux, respectively.

Biomass Estimation
The seasonal cumulative DMP is an indicator of the annual rangeland production [15,[65][66][67], which can be compared to the ground data, that represents the total annual herbaceous production measured in field.
In order to compare satellite data with field samples, EF and DMP were extracted in correspondence with the field sites location in a buffer of 1 km. The 10-day DMP product for the period of July to October, referred to here as JASO, was cumulated to obtain the annual syntheses of dry matter production (DMP JASO ).
The EF was exploited as a water availability factor to correct the satellite estimation of vegetation biomass (DMP).
DMP and EF have different time steps (10 and 8 days, respectively); consequently, monthly values were calculated in order to use the water availability/stress factor in the biomass estimation model.
For EF, the monthly average ( m ) was computed for every month (m) and every site (s): where EF 8D is the estimated water stress from Equation (6), s is the site and n is the cardinality of the 8-day EF data for each month.
For DMP, the monthly sum (DMP m ) was calculated to represent the total dry biomass produced during every month at each site: where DMP 10D is the 10-day biomass estimation product, t is the number of DMP data within the month and s is the site.
Monthly m and DMP m values were than integrated and annually cumulated by the following equation for each site: where EF m and DMP m are the variable obtained from Equations (8) and (9), s is the site and 4 is the number of months in the JASO period. Finally, to quantify the improvement of DMP JASO *, the comparison between observed and estimated values were performed and difference-based statistics [68] together with regression analysis and Akaike information criterion (AIC) [69], Equation (11), were conducted.
where n is the number observed/simulated pairs, MSE is the mean square error and T is the number of inputs in the model. AIC with a lower value indicates whether the increase in the input of a model is compensated for by a significant increase in accuracy.  The intercept of the dry edge follows the typical behavior of West African temperature [70], with lower values during the wet season (June-October) and two peaks during the dry season, the former in April and the latter in November.

Dry and Wet Edge Statistics
The Wet edge intercept has lower value in the wet season and stable, higher values during the dry one. The average slope coefficient shows that during the dry season, the wet edge is generally horizontal (values close to zero), while the dry edge has a high negative slope (values down to −60), as shown by a similar analysis conducted in the Mekong Delta [71].
On the contrary, in the rainy period, the dry edge is almost flat, while the wet edge has a strong positive slope (values up to 60). In general, the coefficients of wet and dry edge follow a seasonal behavior driven by rainfall and incoming solar radiation. Figure 4 shows also three examples of the albedo-LST scatterplots. The first displays the dry season condition with the flat wet edge and the second one the wet condition with the flat dry edge. The last scatterplot displays an intermediate condition at the end of the rainy season, when the two lines are both oblique and the maximum LST is higher.
The maximum albedo value of 0.6 in the scatterplots highlights the presence of high reflective surfaces [72], which correspond to brighter desert areas. These areas are stable through the season; hence, they are present in every plot.
The areas with lower temperature (below 305 K) and lower albedo (below 0.2) correspond to a permanent humid zone, such as the Lake Chad area and the border of the Niger River.
The permanent presence through the years of these two extreme situations allows one to produce a meaningful scatterplot describing the contrast between dry and wet areas, hence guaranteeing the conditions for the application of the method [17,43]. Figure 5 shows the mean EF map obtained from the estimated 448 maps for the period of 2000-2009 (a), together with the RSD (b). As expected, the mean values vary between zero and one, where zero indicates the hyper-arid condition and one the humid area. The areas with a mean rainfall below 200 mm, belonging to the Sahara Desert, were excluded from the analysis, since these areas are not populated and EF estimation makes sense and is useful only on partially vegetated surfaces. Permanent arid areas (EF < 0.2) can be found close to the desert, especially in the Agadez province (Niger) and in the central part of Chad. Both of these areas rely on the -high-risk Sahel's vulnerable zone‖, where the main livelihood activity is transhumant herding [73].

Evaluation of EF Spatial Patterns
The hyper-humid area (EF > 0.7) can be found in correspondence with permanent water bodies, such as Lake Chad [74], Lake Fitri (central Chad) and Lake Kainji (west Nigeria). Furthermore, the woody hills in Nigeria, characterized by a high level of rainfall (more than 1200 mm/year), are generally well humid. The Sahelian belt is characterized by medium-low average values of EF (below 0.5) apart from the river belts: Niger in the west part of study area, Yobe along the Niger-Nigeria border and Chari south of Lake Chad.
The RSD (Figure 5b) is a normalized measure of EF data dispersion. The equation of the RSD is obtained dividing the standard deviation by the mean. The lower percentage indicates a lower variability in the EF time series.
The map highlights areas in red and orange with stable EF (RSD < 30%) from 2000-2009. These areas belong to lakes, rivers and wet regions in central Nigeria, which are also the regions characterized by high EF average values (Figure 5a). Hence, these well-watered areas have maintained their condition across the years analyzed. Vice versa, higher variation in EF values (RSD > 50%, blue and light blue) can be found in the northern Sahel (northern-western Niger and central Chad). In particular, in western Niger, the fossil valleys display a stronger variability of EF data compared to the surrounded rangelands, because of the greater water availability thanks to the morphopedological characteristics, as observed in [75]. The high RDS indicates that the EF data of these areas can vary abruptly, thanks to the strong seasonality (intra-annual variability).
The high EF variability of northern areas in Niger, characterized by the small EF average, can be driven by particularly favorable years (inter-annual variability).
The average EF map has been analyzed by GC classes (Figure 6). The GC classes are sorted from the mainly northern classes (GC_200) to the southern (GC_130), except for the classes of wetland (GC_180) and water body (GC_210). The most common classes are the bare areas (GC_200) and grassland savannah (GC_140). These two classes cover 70% of the entire study area. Figure 6. Percentage of GC classes over the study area (codes and map color are reported) and the statistics of EF data for each LC classes (average (AVG) and relative standard deviation (RSD)). Red and green indicate land cover with a lower of a higher EF average, respectively.
On average, the GC class with the highest EF value (EF = 0.83) is water bodies (GC_210). Among the vegetation classes, only irrigated crops (GC_10), forest (GC_60) and wetland have a mean EF greater than 0.6. The most arid classes (GC_140 and GC_200), with a mean EF lower than 0.4, describe the typical landscape of the northern Sahel [50].
This analysis shows that the spatial patterns of EF data (long-term average) are in agreement with the well-known climatic and landscape features of these areas. A similar analysis conducted in China [21], Europe [26] and Africa [22] demonstrated that EF maps build up spatial and temporal patterns coherent with the presence of different vegetated surfaces, different climatic conditions and different seasonal behavior of vegetation. Figure 7 presents the time series of net radiation, ET and EF measured at the Wankama eddy covariance tower (black lines) and the satellite-derived time series of EF (red dashes), RFE (blue bars),   Vertical black lines indicate the average Sahelian wet season as being from July to October (JASO). The zero value of the satellite EF estimation, due to cloud contamination or other atmospheric interference in the data, was masked out from this analysis. Figure 7a shows the time series of remote sensed and measured variables for the year, 2005. The first eddy measurement was recorded in June (doy 160), after the beginning of rain. ET shows the peak (>4 mm/day) in August, as well as net radiation. RFE shows an early start of the rainy season doy doy compared to the JASO, with an intense rainfall period of 60 mm in May (doy 155). In total, 524 mm fell in 2005. The red dashes indicate the eight-day period of satellite EF estimation from Equation (6) together with the in situ calculated EF from Equation (7). Both of the EF time series show higher values in the rainy season and drops in correspondence with the low ET value (e.g., doy 210 and 240). MODIS-derived EF decreases smoothly after doy 270, as happens for ET.

Temporal Dynamics of the Variables
The vegetation behavior, highlighted by NDVI, shows the start of the season around doy 200 (19 July), about 50 days after the start of rainfall, because of the necessary time for germination [75]. NDVI has a specular behavior compared to albedo, as expected from the progressive cover of bare soil due to vegetation growth. The last two time series in Figure 7a display albedo and LST data. Both show a high value during the dry season, indicating a warm and bare surface. The rainy season has an average LST of 308 K (~35 °C), lower than the dry season average (311 K), because incoming energy during is exploited by evaporative and transpirative processes. Figure 7b shows the same variables for 2006. The rainy period is shorter and less abundant compared to the previous one, with 430 mm of total rainfall. The estimated EF reaches a peak of 0.8 at doy 240 (28 August). The main EF drop is visible (doy 210) in correspondence with the drier period of the wet season, between the two main rain events. Both EF and ET rapidly decrease their values at the end of the wet season (doy 270). Higher vegetation growth occurs between August and September, and NDVI shows the presence of vegetation also in November-December (doy 300-360, NDVI ~0.2), even if EF and ET show that the area is completely dry.
The temporal behaviors of field measurements and satellite-derived data for 2005 and 2006 display high variability between dry and wet months. The 2005 wet season had an early start, while 2006 had a very late start, as well as an earlier end. Hence, the two years had different seasonality in terms of rainfall amount and distribution [62]. Among the several satellite-derived variables, estimated EF shows a higher correlation with estimated rainfall (data not shown), as expected from previous field studies [36,37,64,70], and in general, the estimated EF looks to be in accordance with the ET behavior and eddy covariance-derived EF. The temporal behavior of the EF variable is more noisy compared to the time series of other satellite-derived variables and hardly zero also in the absence of rainfall [39], as also displayed by eddy-derived EF. Both

Correlation Analysis with ET
In order to evaluate the reliability of EF as a moisture indicator, a correlation analysis has been conducted between satellite EF estimation (y-axis) and ET measured by the eddy covariance tower (x-axis) (Figure 8).
The EF resulted in being significantly correlated to ET (p < 0.001), with a regressive coefficient of 0.54 pooling together the two years (2005)(2006). ANCOVA analysis reveals that single year correlations (2005, r 2 = 0.62; 2006, r 2 = 0.45) were not significantly different (p < 0.05). This correlation is biased by estimated EF in the late, dry season (January-May), when no rain and no vegetation are present, confirming that EF is noisy in the dry season [39]. As expected the measured net radiation is better correlated with ET (r 2 = 0.64), since it represents the climatic driving force of evaporative and transpirative processes. In order to investigate if EF can improve the capability to explain the variance of ET, a multiple regression was performed between ET as a dependent variable and two independent variables, the measured Rn and the simulated EF.
Result shows that both the explanatory variables significantly contribute to the explanation of ET variability (70% of the total variance). Rn resulted in being more important, explaining about 64% of the total variance (p < 0.001), and EF significantly improved the model with a further 6% of variance explanation (p < 0.01). These results indicate that EF estimated with low resolution satellite data is well correlated with the field measured flux and gives a statistically significant contribution to the explanation of ET variability. It is important to remember that the EF data is derived by 1-km albedo and LST products; this aspect can strongly limit the comparison with field data acquired on small plots in a heterogeneous environment.

Biomass Estimation Improvements Using EF Correction
The results of previous analysis confirmed the validity of EF as a moisture indicator supporting the idea of using this satellite estimation as a water stress factor in a radiation use efficiency model. Previous studies, exploiting only field-based EF, demonstrated that EF can be exploited as a water stress efficiency factor [41].
To assess this contribution, the performance of operational products (DMP JASO ) and biomass estimation corrected by EF (DMP JASO *) were compared with available annual production data over three test sites in Niger.
In Figure 9a are shown the three sites' specific correlations between the available field data and DMP JASO . The three sites show different correlations: in particular, Site 1 (black dots) presents little correlation (r 2 = 0.49, intercept = 1300, slope = 0.3); Site 2 (blue squares) shows an average correlation (r 2 = 0.51, intercept = 700, slope = 1.1); and Site 3 (red triangles) has a high correlation (r 2 = 0.66, intercept = 400, slope = 0.3). All three sites have the typical Sahelian biomass production [76], ranging from 100 (kg· ha −1 ), in adverse years, to 20-times higher production in favorable climatic conditions. Results demonstrate that the DMP JASO is able to detect the field biomass variability with site-specific, good correlation; however, the analysis of intercept and slope variability across sites indicates that the model is not able to give a robust quantitative biomass estimation. Indeed, the DMP algorithm does not take into account distinct efficiency factors in the conversion of light into biomass among different vegetation types. It should be reminded that, despite the three test sites featuring the same land cover and eco-region, the actual floristic composition and ecological characteristics could be much more different.
In Figure 9b are shown the effect of the EF contribution (DMP JASO *) over the three sites. The plots show a general increase in the capacity of the remote sensing estimation in each site to detect the variability of the field measurements if water stress is taken into account, as indicated by the increasing of regression coefficients. Moreover, in particular, the EF has reduced the overestimation of the model for poorly productive years, as shown by intercepts closer to zero.
Due to the observation of site-specific DMP product performance, in order to directly compare the two biomass estimations, satellite products and field data were normalized for each site. The normalized data allows one to remove the effect of local differences in the relation between satellite outputs and field biomass, visualizing only the overall model capability to detect the field data variance, rather than absolute values. Data were standardized and converted to z-scores by subtracting from each value the site average and then dividing the result by the standard deviation. In the analysis of time series, the z-score is a dimensionless quantity adopted to convert variables with different scales to a common domain [10,77].
In Figure 9c are shown the normalized data, both for DMP JASO (gray dots) and DMP JASO * (black dots). The data close to zero are near the population average, while data values below or above zero indicate a positive or a negative anomaly, respectively. The top right and bottom left corners indicate that years were estimated, and the measured variables' data are in agreement.
The correlation coefficient of the normalized DMP JASO * (r 2 = 0.73, p < 0.001) indicates that there is a significative increase in the capacity of the remote sensing estimation to explain the variance of annual field biomass measurements if water stress (EF) is taken into account.
This result is in accordance with previous work [41], even if the analysis was conducted at a monthly time step using EF derived with MODIS data (LST and albedo), rather than with field-measured EF and MODIS EVI at an eight-day time step.
Finally, AIC was calculated in order to evaluate whether the increase in the input of the model compared to the basic DMP was compensated for by a significant increase in accuracy (a lower AIC value indicates a convenient model improvement) [69]. Despite the correction, proposed to increase the number of inputs in the biomass estimation, the usefulness of the EF approach (DMP JASO *) is confirmed by the improved model performance, indicated by the higher correlations shown in Figure 9c and the lower AIC value (106) compared with the one obtained with DMP JASO (112).

Conclusions
The work exploited an automatic procedure to calculate multitemporal evaporative fraction maps from low resolution albedo and land surface temperature satellite data over Niger and Chad. Up to now, this is the first time that multiyear (2000-2009), eight-day maps of the evaporative fraction were produced from low resolution satellite data and analyzed for the West African Sahel. The adopted methodology, based on previous scientific works and well suited for semi-arid areas, allowed producing maps able to identify patterns of wet and dry condition, which are coherent with the main ecological features related to land cover classes and precipitation regimes.
The satellite estimation of the evaporative fraction, despite the uncertainty related to the 1-km resolution of the data, resulted in being correlated with the measurements of evapotranspiration (r 2 = 0.54, p < 0.001) acquired for two years (2005)(2006) by an eddy flux tower in Niger. The total variance of evapotranspiration is mainly explained by the measured net radiation (64%, p < 0.001), while the estimated evaporative fraction significantly improves the model with a further 6% of variance explanation (p < 0.01). These results demonstrate that the satellite-derived evaporative fraction is a reliable indicator of moisture, useful for savannah status monitoring.
We further tested the use of the evaporative fraction as a water availability indicator to improve the accuracy of an operational remote sensing product of biomass estimation based on the radiation use efficiency concept. When the satellite-derived evaporative fraction is used as an indicator of water stress in the model, the correlation between annual biomass ground measurements and satellite estimations, for 19 samples over three sites, significantly improves (r 2 = 0.73, p < 0.001) compared to the performance of the basic satellite product (r 2 = 0.54, p < 0.001). The appropriate water efficiency term derived from optical and thermal remote sensing data represents an advancement over previous studies conducted using only the evaporative fraction derived by in situ eddy covariance data.
These findings are encouraging for the monitoring of biomass over wide savannah areas using a satellite-based approach. Future studies are needed to better parameterize the radiation use efficiency model and to calibrate existing products over different ecosystems, in order to take into account the limiting factors and efficiency in the conversion of light into biomass.