Evaluating water controls on vegetation growth in the semi-arid sahel using field and earth observation data

: Water loss is a crucial factor for vegetation in the semi-arid Sahel region of Africa. Global satellite-driven estimates of plant CO 2 uptake (gross primary productivity, GPP) have been found to not accurately account for Sahelian conditions, particularly the impact of canopy water stress. Here, we identify the main biophysical limitations that induce canopy water stress in Sahelian vegetation and evaluate the relationships between ﬁeld data and Earth observation-derived spectral products for up-scaling GPP. We ﬁnd that plant-available water and vapor pressure deﬁcit together control the GPP of Sahelian vegetation through their impact on the greening and browning phases. Our results show that a multiple linear regression (MLR) GPP model that combines the enhanced vegetation index, land surface temperature, and the short-wave infrared reﬂectance (Band 7, 2105–2155 nm) of the moderate-resolution imaging spectroradiometer satellite sensor was able to explain between 88% and 96% of the variability of eddy covariance ﬂux tower GPP at three Sahelian sites (overall = 89%). The MLR GPP model presented here is potentially scalable at a relatively high spatial and temporal resolution. Given the scarcity of ﬁeld data on CO 2 ﬂuxes in the Sahel, this scalability is important due to the low number of ﬂux towers in the region.


Introduction
The Sahel is an arid and semi-arid region that stretches from the Atlantic Ocean in the west to the Red Sea in the east and separates the hyper-arid Sahara desert from the sub-humid and humid regions to the south ( Figure 1). The Sahel has experienced a prolonged dry period from the mid-1960s through the late 1980s in which there were severe droughts that resulted in humanitarian crises [1]. Recovery from this dry period was reported by Eklundh and Olsson [2], who observed strong increases in seasonal satellite-derived normalized difference vegetation index (NDVI) from the mid-1980s onwards. This increase in vegetation greenness began to be referred to as the "greening of the Sahel" [3], and is the result of increases in both herbaceous [4] and tree cover [5]. Seaquist et al. [6] translated this greening into sequestered carbon (C) and found that 51 megatonnes of C (MtC) per year where taken up by Sahelian vegetation between 1982 and 1999 resulting in a net increase of 918 MtC Gross primary productivity (GPP) is the total amount of C plant extract from the atmosphere through photosynthesis. Some of this C goes to maintaining plant tissue, and is thus lost through autotrophic respiration (Ra). The remaining C is stored as phytomass (net primary productivity, NPP = GPP − Ra). The capacity of Sahelian ecosystems to provide essential food, fuel, feed and fiber is a function of available NPP [8]. Since these ecosystem services are essential, evaluating the environmental controls that modulate GPP dynamics is necessary for accurate accounting of primary productivity. The Sahel has a single growing season that starts in July and ends in October [9] with considerable inter-annual variability in the spatial distribution and quantity of rainfall [10,11]. The driest parts of the northern Sahel receive an annual average of 150 mm of rain, while the southern parts receive an annual average of ~750 mm [12] (Figure 1).
The Sahel ( Figure 1) is dominated by plants that have the C4 photosynthetic pathway [13], which are adapted to warm, arid environments and are composed mainly of grasses, herbs and crops. The mean tree canopy cover is approximately 7.3% and comprises trees that use the C3 photosynthetic pathway [14,15]. It is well known that moisture availability controls C fluxes in drylands such as the Sahel, and several studies have attempted to explain the underlying mechanisms of its modulation of primary productivity in these regions [7,[16][17][18][19][20][21]. Merbold et al. [22] found that mean annual rainfall is strongly correlated with maximum photosynthetic capacity and is the predominant factor driving C fluxes across Africa. With rainfall, the greening phase commences (Figure 2), and soil moisture is replenished, which impacts the amount of energy partitioned into evapotranspiration [21,23,24]. Rainfall also increases humidity, which lowers the difference between the vapor pressure deficit inside the leaf and that of the air. This difference in vapor pressure deficit was found to be a key factor affecting stomatal conductance of Sahelian plants [25,26]. The browning phase ( Figure 2) begins with a decrease in soil moisture and increase in both surface temperature and vapor pressure deficit, which triggers the closure of the stomata to prevent water loss through transpiration. The closure of the stomata prohibits the flow of CO2 into the leaf and thus reduces GPP.
Most studies covering the Sahel base their results on a handful of sites, due to the scarcity of data on C fluxes over the region's 3.3 million km 2 of surface area [27]. Thus, Earth observation is an Gross primary productivity (GPP) is the total amount of C plant extract from the atmosphere through photosynthesis. Some of this C goes to maintaining plant tissue, and is thus lost through autotrophic respiration (Ra). The remaining C is stored as phytomass (net primary productivity, NPP = GPP − Ra). The capacity of Sahelian ecosystems to provide essential food, fuel, feed and fiber is a function of available NPP [8]. Since these ecosystem services are essential, evaluating the environmental controls that modulate GPP dynamics is necessary for accurate accounting of primary productivity. The Sahel has a single growing season that starts in July and ends in October [9] with considerable inter-annual variability in the spatial distribution and quantity of rainfall [10,11]. The driest parts of the northern Sahel receive an annual average of 150 mm of rain, while the southern parts receive an annual average of~750 mm [12] (Figure 1).
The Sahel ( Figure 1) is dominated by plants that have the C 4 photosynthetic pathway [13], which are adapted to warm, arid environments and are composed mainly of grasses, herbs and crops. The mean tree canopy cover is approximately 7.3% and comprises trees that use the C 3 photosynthetic pathway [14,15]. It is well known that moisture availability controls C fluxes in drylands such as the Sahel, and several studies have attempted to explain the underlying mechanisms of its modulation of primary productivity in these regions [7,[16][17][18][19][20][21]. Merbold et al. [22] found that mean annual rainfall is strongly correlated with maximum photosynthetic capacity and is the predominant factor driving C fluxes across Africa. With rainfall, the greening phase commences (Figure 2), and soil moisture is replenished, which impacts the amount of energy partitioned into evapotranspiration [21,23,24]. Rainfall also increases humidity, which lowers the difference between the vapor pressure deficit inside the leaf and that of the air. This difference in vapor pressure deficit was found to be a key factor affecting stomatal conductance of Sahelian plants [25,26]. The browning phase ( Figure 2) begins with a decrease in soil moisture and increase in both surface temperature and vapor pressure deficit, which triggers the closure of the stomata to prevent water loss through transpiration. The closure of the stomata prohibits the flow of CO 2 into the leaf and thus reduces GPP. radiation within the spectral range of 1850-2130 nm was sensitive to soil volumetric water content. Consequently, there is potential utility of this spectral range in C cycle studies that focus on Sahelian settings. This study has two objectives: (1) To identify the relative strengths of biophysical limitations that reduce CO2 uptake in the Sahel; and (2) evaluate empirical relationships between Earth observation-derived spectral products that can account for these limitations to better explain the variability in eddy covariance (EC) GPP using Earth observation data. Conceptual diagram of the greening and browning processes present in the Sahel. The two peaks represent the uptake of CO2 and the increase in gross primary productivity (GPP). The greening phase begins with the start of the rainy season and the increase in plant-available water (PAW, Section 3.3.1). During the greening phase vapor pressure deficit (VPD, Section 3.3.2) decreases and so does land surface temperature (LST). The beginning of the browning phase starts with a reduction in PAW and increase in VPD and LST.

Field Sites
We used three eddy covariance sites located in Sudan, Niger and Senegal. All three sites are within a narrow latitudinal band between 13°N and 15°N ( Figure 1). A summary of the sites is presented below and summarized in Table 1.

Figure 2.
Conceptual diagram of the greening and browning processes present in the Sahel. The two peaks represent the uptake of CO 2 and the increase in gross primary productivity (GPP). The greening phase begins with the start of the rainy season and the increase in plant-available water (PAW, Section 3.3.1). During the greening phase vapor pressure deficit (VPD, Section 3.3.2) decreases and so does land surface temperature (LST). The beginning of the browning phase starts with a reduction in PAW and increase in VPD and LST.
Most studies covering the Sahel base their results on a handful of sites, due to the scarcity of data on C fluxes over the region's 3.3 million km 2 of surface area [27]. Thus, Earth observation is an important tool for large-scale studies of the GPP of Sahelian ecosystems. The only global model of satellite-driven GPP estimates is the MOD17 production efficiency model [28], which is based on the light-use efficiency concept [29]. However, this dataset has been shown to considerably underestimate GPP over semi-arid Sahelian ecosystems [21,30]. Recent work by Sadeghi et al. [31] found that the shortwave infrared spectral range of 2105-2155 nm, corresponding to band 7 in the moderate-resolution imaging spectroradiometer (MODIS) satellite sensor, provides optimal sensitivity to variations in soil moisture. Furthermore, aerosol effects are negligible because most aerosol particulates are smaller than that wavelength range [32]. The drying and wetting processes that influence vegetative growth could be captured by satellite sensors that cover this spectral range because soil moisture at the top 1-2 cm of soil significantly influences soil surface reflectance at these wavelengths [33,34]. Another recent study by Tian and Philpot [35] found that shortwave infrared radiation within the spectral range of 1850-2130 nm was sensitive to soil volumetric water content. Consequently, there is potential utility of this spectral range in C cycle studies that focus on Sahelian settings. This study has two objectives: (1) To identify the relative strengths of biophysical limitations that reduce CO 2 uptake in the Sahel; and (2) evaluate empirical relationships between Earth observation-derived spectral products that can account for these limitations to better explain the variability in eddy covariance (EC) GPP using Earth observation data.

Field Sites
We used three eddy covariance sites located in Sudan, Niger and Senegal. All three sites are within a narrow latitudinal band between 13 • N and 15 • N ( Figure 1). A summary of the sites is presented below and summarized in Table 1.  Table 1). The landscape around the site is a typical Sahelian savanna, comprised of sparse trees, mainly Acacia senegal and Acacia nilotica, with a canopy cover of approximately 7%. The ground cover comprises annual grasses, primarily Cenchrus biflorus, Eragrostis tremula, and Aristida pallida. The sandy soils are poor in nutrients, have low soil organic C, and low cation exchange capacity [39]. A complete description of Demokeya is provided in Ardö et al. [36].

Wankama, Niger
The Wankama site is divided into two sub-sites, Wankama Millet (13.644 • N, 2.629 • E) and Wankama Fallow (13.647 • N, 2.633 • E), both of which are located in southwest Niger and within close proximity to each other. Mean annual air temperature is 30 • C and mean annual precipitation is 479 mm (Table 1). Only the fallow site has been used in this study. This site is composed of shrub and herbaceous layers; the shrub layer is primarily composed of Guiera senegalensis and the herbaceous layer is dominated by Zornia glochidiata [40]. The soils are mostly sandy with low nitrogen and phosphate content. A complete description of Wankama is provided in Cappelaere et al. [37].

Dahra, Senegal
Dahra (15.402 • N, 15.432 • W) is located in the Louga province of northern Senegal. Long-term mean annual air temperature is 29 • C and mean annual precipitation is 416 mm ( Table 1). The vegetation around the site is grazed by livestock and dominated by annual grasses, particularly Aristida adscensionis, Zornia latifolia, Eragrostis tremula, Dactyloctenium aegyptium, and Cenchrus biflorus. The canopy cover is approximately 3% and comprises Acacia Senegal, Acacia tortilis, and Balanites aegyptiaca. The soils are sandy with low water holding capacity and organic matter content. A complete description of Dahra is provided in Tagesson et al. [38].

Eddy Covariance Gross Primary Productivity
The eddy covariance (EC) systems at all three sites are equipped with LI7500 open path infrared CO 2 /H 2 O analyzers (LI-COR Inc., Lincoln, NE, USA) and GILL R3 triple-axis sonic anemometers (GILL Instruments, Lymington, UK). Eddy covariance data were recorded at 20 Hz and averaged over 30-min periods. The EC method measures net ecosystem exchange of CO 2 (NEE) and following the approach in Tagesson et al. [41], NEE was partitioned into GPP and ecosystem respiration (R eco ) Remote Sens. 2017, 9,294 5 of 20 using a non-linear asymptotic regression with incoming photosynthetically active radiation and vapor pressure deficit as independent variables. Gaps in the time series of NEE, GPP and R eco were consequently gap-filled, again following the method outlined in Tagesson et al. [41].

Climatic Variables
Air temperature ( • C) and relative humidity (%) at 2 m were monitored using MP100A Temperature and Relative Humidity Probe (Rotronic) in Demokeya, with Vaisala HMP45C probes (Vaisala Oyj, Helsinki, Finland) in Wankama, and Campbell CS215 (Campbell Scientific, Logan, UT, USA) in Dahra. Precipitation (mm) was recorded using ARG100 tipping buckets (Campbell Scientific, UT, USA) at all three sites. Volumetric soil moisture was recorded using CS616 water content reflectometers (Campbell Scientific) in Demokeya and Wankama, and HH2 probe (Delta T Devices) in Dahra. These parameters were recorded every 10-30 s and averaged for every 30 min. Measurement depths varied with site and were dependent on the field campaign. Volumetric soil moisture was summed from top of soil to 50 cm depth in Dahra and Wankama, and to 60 cm depth in Demokeya in order to compute plant-available water (see Section 3.3.1).

Earth Observation Data
The moderate-resolution imaging spectroradiometer (MODIS) sensor on board NASA's Terra and Aqua satellites has a viewing swath width of 2330 km and images the entire surface of the Earth every one to two days. The MCD43A4 nadir bidirectional reflectance distribution function adjusted reflectance (NBAR) product, which is produced every 8 days within 16 days of acquisition, is preferable over the other surface reflectance products (MOD09A1/MYD09A1) because it is adjusted using a bidirectional reflectance distribution function to model at-nadir values [42]. The Collection 5.1 MCD43A4 NBAR Level 3 and MOD17 8-day GPP product (MOD17A2) products were downloaded for each site from the Oak Ridge National Laboratory Distributed Active Archive Center (ORNL-DAAC, daac.ornl.gov/modisglobal). Band 7 of the MCD43A4 NBAR product (henceforth, MODIS NBAR Band 7 or simply Band 7) covers the shortwave infrared wavelength range of 2105-2155 nm that is crucial for capturing sensitivity to variations in soil moisture [31]. These data are provided as ASCII files containing observations within a specified radius around a particular point of interest. We selected a 3 × 3 km area around each flux tower site based on footprint analysis conducted in Demokeya by Sjöström et al. [43] and in Dahra by Tagesson et al. [44]. Land surface temperature (LST) has been found to strongly influence ecosystem respiration [45,46] and has been used estimate vapor pressure deficit [47]. Sims et al. [48] used LST to characterize temperature and drought stress in a modeling framework that used MODIS-enhanced vegetation index (EVI) as a predictor of GPP. In order to test the applicability of LST for improving GPP modeling, we downloaded the 8-day MOD11A2/MYD11A2 Level 3 LST product (Collection 5.1) from the ORNL-DAAC database (daac.ornl.gov/modisglobal).

Methodology
This section details the techniques that were used to derive three field-based variables: plant-available water, vapor pressure deficit and the antecedent precipitation index, and one Earth observation-based variable: the enhanced vegetation index. The rationale behind the selection of each variable is also described. Finally, the statistical methods that were chosen to construct and evaluate the models are detailed in the concluding subsection.

Plant-Available Water
Plant-available water (PAW) is the amount of water present in the soil that can be extracted by roots. PAW is a function of soil type, soil water content at field capacity (moisture left over after percolation) and permanent wilting point (soil moisture that is unavailable to plants). It is an important Remote Sens. 2017, 9, 294 6 of 20 parameter in the terrestrial water cycle and may have a considerable influence on GPP [49]. PAW was calculated as: where PAW is plant-available water (mm); SWC is volumetric soil water content at field capacity (m 3 m −3 ); PWP is the soil texture-dependent permanent wilting point from Table 2 expressed as a dimensionless fraction (m 3 m −3 ); and D is the depth (mm) at which the soil moisture measurements were made. The PWP is a biophysical parameter that quantifies the condition where the force exerted by a plant to remove water from the soil (−1500 kPa) is countered by the forces binding the water to the soil [50]. At this point plant roots cannot extract further water from the soil and sustain growth, thus leading to wilting.

Vapor Pressure Deficit
When plants transpire, the mixture of air and water exiting the stomata is saturated at a relative humidity of~100% [53]. The maximum amount of water vapor the air can hold at a particular temperature is a function of the temperature itself, so there is potential for higher transpiration at higher temperatures. The climate of the Sahel is generally hot, with a mean annual air temperature of 30 • C across the three sites. The average relative humidity (RH) across the three sites is 18% in the dry season and 65% in the growing season according to the field measurements. Vapor pressure deficit (VPD) [54] is the difference between the amount of water in the air and the maximum amount of water the air can hold when it is saturated, and is a limiting factor for Sahelian GPP [25,26,55]. VPD was calculated from field-measured air temperature (T a , • C) and relative humidity (RH, %) following the approach described in Ward et al. [56]: where e s is the saturation vapor pressure (kPa) at a certain T a . Then, the actual vapor pressure (e a , kPa) is calculated from RH and e s : Finally, VPD (kPa) is estimated as the difference between the two:

Antecedent Precipitation Index
The timing, quantity and effects of previous rainfall on vegetation are important because it takes time for water to percolate through soil and become available for plants. When precipitation occurs, soil moisture conditions evolve as a function of its current degree of saturation. Antecedent precipitation index (API) [57] has been previously used to characterize the influence of past rainfall events on vegetation [58]. The formulation of API used here follows Heggen [59]: where API is the antecedent precipitation index in mm per 8 days; P t is the observed precipitation amount on period t; the decay constant, k, ranges between 0.80 and 0.98 [60] and a value of 0.90 has been applied in this study; a is the number of antecedent days.

Enhanced Vegetation Index
The Enhanced Vegetation Index (EVI) [61,62] utilizes three spectral bands that summarize radiometric and biophysical vegetation characteristics. EVI includes the blue band in addition to the vegetation-sensitive red and near-infrared bands. A set of coefficients and the blue band enhances the vegetation signal by reducing the influence of soil reflectance and atmospheric scattering. Sjöström et al. [21] and Ma et al. [63] found that EVI follows the seasonal dynamics of EC GPP better than the MODIS-derived GPP in Sahelian and Australian xeric savannas, respectively.

Statistical Analysis
Data processing, statistical analysis and visualization were performed in R 3.1.1 (www.r-project.org). Both linear and multiple linear regression (MLR) were used to examine the relationships between VPD, PAW, LST, EVI, NBAR Band 7, and EC GPP. The relationships were used to build GPP models composed of field metrics of water stress and vegetation indices as input data. Additionally partial correlations were performed on both the field and Earth-observation variables during the greening and browning phases using Spearman's rank order correlation [64]. This was done to assess the relationship of each variable with EC GPP while keeping the influence of the other variables constant. Within each year, the greening phase was delineated as the period from the lowest to the highest GPP value, and the browning was delineated as the following period from maximum GPP to its lowest value. The coefficient of determination (R 2 ) was calculated as a measure of the amount of EC GPP variance explained by each set of predictor variables. Bayesian information criterion (BIC) [65] was chosen to identify the model which best describes the EC GPP data: where L is the maximum value of the likelihood function of the model, q is the total number of parameters and n is the number of sample points. BIC considers both the goodness of fit and the number of parameters that achieve a certain degree of fit by levying a penalty term qln(n) on increasing the number of parameters to prevent over-fitting. Root-mean-square error (RMSE) was calculated to evaluate the performance of each model output relative to EC GPP. RMSE calculates the square root of the variance and smaller values denote better model performance. An RMSE of 0.0 indicates perfect simulation of the EC GPP data.
Remote Sens. 2017, 9, 294 8 of 20 where PRED is the model-estimated GPP (g C m −2 d −1 ), OBS is the EC GPP (g C m −2 d −1 ), and n is the number of sample points.

Seasonal Dynamics and Inter-Annual Variability of EC GPP, PAW, VPD and API
Growing season average EC GPP was highest in Dahra at 8.6 g C m −2 d −1 , followed by Demokeya at 3.9 g C m −2 d −1 and Wankama Fallow with 3.5 g C m −2 d −1 . EC GPP was tightly coupled with climate across all sites (Figure 3). The greening phase was dominated by a rapid decrease in VPD and an increase in the amount of PAW. Growing season EC GPP was attained across all sites when PAW was generally above 25 mm (~0.04 m 3 m −3 ) and when VPD was below 2 kPa, which is comparable to studies conducted in similar environments [22,66]. The decline in PAW and the onset of high VPD during times of drought reduces plant photosynthetic capacity by causing closure of stomata to prevent moisture loss [67]. Thus, a decrease in moisture during the growing season, as happened in Dahra in 2011, where there was 42% decrease in rainfall and 46% decrease in soil moisture from the previous year, could cause a reduction in GPP. Indeed, EC GPP in Dahra during the 2011 growing season was 72% less than the previous year. A similar pattern of decline was observed in Demokeya during the 2009 growing season when there was a 25% decrease in rainfall, 14% decrease in soil moisture, and a 9% decrease in GPP from the previous year (Figure 3a). When rainfall resumes to previous levels, as happened in 2012 in Dahra (Figure 3c), the herbaceous vegetation respond rapidly to changes in the soil water regime resulting in increased C uptake [13]. It has been shown that the terrestrial biosphere can retain "memory" of past wet or dry conditions through soil moisture or the vegetation itself [68,69]. In this study, the observed speed of vegetation response to the resumption of rainfall could be due to this land memory effect.

Seasonal Dynamics and Inter-Annual Variability of EC GPP, PAW, VPD and API
Growing season average EC GPP was highest in Dahra at 8.6 g C m −2 d −1 , followed by Demokeya at 3.9 g C m −2 d −1 and Wankama Fallow with 3.5 g C m −2 d −1 . EC GPP was tightly coupled with climate across all sites (Figure 3). The greening phase was dominated by a rapid decrease in VPD and an increase in the amount of PAW. Growing season EC GPP was attained across all sites when PAW was generally above 25 mm (~0.04 m 3 m −3 ) and when VPD was below 2 kPa, which is comparable to studies conducted in similar environments [22,66]. The decline in PAW and the onset of high VPD during times of drought reduces plant photosynthetic capacity by causing closure of stomata to prevent moisture loss [67]. Thus, a decrease in moisture during the growing season, as happened in Dahra in 2011, where there was 42% decrease in rainfall and 46% decrease in soil moisture from the previous year, could cause a reduction in GPP. Indeed, EC GPP in Dahra during the 2011 growing season was 72% less than the previous year. A similar pattern of decline was observed in Demokeya during the 2009 growing season when there was a 25% decrease in rainfall, 14% decrease in soil moisture, and a 9% decrease in GPP from the previous year (Figure 3a). When rainfall resumes to previous levels, as happened in 2012 in Dahra (Figure 3c), the herbaceous vegetation respond rapidly to changes in the soil water regime resulting in increased C uptake [13]. It has been shown that the terrestrial biosphere can retain "memory" of past wet or dry conditions through soil moisture or the vegetation itself [68,69]. In this study, the observed speed of vegetation response to the resumption of rainfall could be due to this land memory effect. The seasonal variability of the field parameters, PAW, VPD and EC GPP, was fairly consistent across all sites (Figure 3). However, Dahra had the highest average EC GPP during the growing season (8.6 g C m −2 d −1 ) despite having similar climatic and subsurface conditions as the other two sites (Table 1). A recent study by Tagesson et al. [70] provided two plausible reasons for the higher The seasonal variability of the field parameters, PAW, VPD and EC GPP, was fairly consistent across all sites ( Figure 3). However, Dahra had the highest average EC GPP during the growing season (8.6 g C m −2 d −1 ) despite having similar climatic and subsurface conditions as the other two sites (Table 1). A recent study by Tagesson et al. [70] provided two plausible reasons for the higher photosynthetic capacity at Dahra: (1) A total of 80% of the vegetative cover at Dahra is comprised of herbaceous C 4 plants, signifying a higher concentration of plants that are more productive under optimal climatic conditions (i.e., during the growing season); and (2) intense grazing disturbance causes plants to develop strategies that allocate more C to leaves thereby increasing their leaf area index and leading to increase in absorbed photosynthetically active radiation and C assimilation. A third plausible reason for the high EC GPP at Dahra is linked to the increase in relative humidity which ranges from 9% in the dry season to 63% in the growing season (Table 1). This is connected to the movement of the inter-tropical convergence zone (ITCZ) and the West African Monsoon, which transports moist air from the Gulf of Guinea to West Africa [13,38,71]. This large influx of humid air could allow the stomata to remain open longer during the growing season, thus enabling enhanced C uptake without increased water loss through transpiration. Growing season (July-October) API in Dahra was 153% higher than Demokeya and 57% higher than Wankama Fallow, and had higher intra-seasonal variability (standard deviation = 171%). This is also probably due to West African Monsoon, which causes higher amounts of rainfall at Dahra [71][72][73][74].

Relationship between EC GPP, PAW, VPD, and API
Cross-site relationships of PAW and VPD with EC GPP were fairly moderate (R 2 = 0.36 and 0.43, respectively). The relationships at the individual sites were varied with R 2 values of VPD ranging between 0.59 and 0.75 and those of PAW between 0.59 and 0.76 (Table 3). API was the worst-performing variable, averaging a cross-site R 2 of 0.33. This is probably due to the fact that rain events during the growing season were sporadic and API could not capture the lag effect each event had on EC GPP. The combination of PAW and VPD explained the largest variance across all three sites (R 2 = 0.47, RMSE = 2.06 g C m −2 d −1 ), with the highest R 2 and lowest RMSE at Wankama Fallow (R 2 = 0.83, RMSE = 0.77 g C m −2 d −1 ) ( Table 3).
An overview of the relationship between EC GPP, VPD and PAW across all sites is shown in Figure 4. The dry season is characterized by high VPD (>2 kPa), which is linked to the reduction in evapotranspiration due to low PAW. With the reduction/closure of stomatal conductance, plants deactivate metabolic activity in the shoots to reduce consumption of water (and subsequent transpiration) while simultaneously enhancing uptake of water and nutrients by the roots to mitigate the effect of the dry season [75]. In the wetter savanna systems of the humid region (>750 mm of mean annual precipitation, MAP), it has been shown that a considerable amount of C is stored in the roots at the start of the dry season and is subsequently used by the herbaceous vegetation to re-sprout at the start of the next growing season [76]. If the dry season is intense, prolonged, or both, this memory effect allows vegetation to tap into these C reserves and maintain root respiration [77]. A recent global study by Murray-Tortarolo et al. [78] lends support to this, finding that the intensity and duration of the dry season has a larger impact on annual primary productivity than increased rainfall in the rainy season. Thus, a similar mechanism may take place in the poorer soils of the Sahel, where the herbaceous species are specialized to grow quickly at the beginning of the rainy season [13]. These subsurface mechanisms can in turn be influenced by anthropogenic activity as soil moisture amount and availability are influenced by land management practices [36,79].
When the rainy season commences, not only is soil water replenished and root water uptake increased, but VPD is reduced due to humid air masses from the northward movement of the ITCZ. In Wankama Fallow, maximum EC GPP is reached when PAW is greater than 125 mm and VPD is below 1.5 kPa, while in Demokeya maximum EC GPP occurs when PAW is above 90 mm and VPD is below 2 kPa. At Dahra, maximum EC GPP was reached at VPD levels similar to Demokeya and Wankama Fallow, however, PAW was relatively low compared to the other two sites at~60 mm. The partial correlation analysis revealed that the increase in C uptake during the greening phase, shortly after the onset of the first rains, is governed by the availability of PAW and a reduction in VPD (Table 4). The increase in soil moisture also decreases LST (Spearman's Rho, r s = −0.28) due to evaporative cooling. These are further illustrated by scatterplot in Figure 5. The browning phase is characterized by a steep decrease in GPP and a reduction in PAW due to a cessation of the rains. The relationship of EC GPP, VPD and PAW were generally strong during both the greening and browning phases ( Figure 5). The mechanism by which VPD and PAW interact is further illustrated in Figure 6, which uses the 2009 growing season in Demokeya as an example. The first rains occurred on July 4, however, the relative humidity began to increase from a mean of 15% in April and May, which is typical of the dry season, to 32% in June. Between 4 July and 1 September (the larger shaded area in Figure 6), the mean relative humidity was 64%. The effect of the increase in relative humidity, and decrease in VPD, a full month before the first rains is particularly interesting. This can play the role of an anticipatory mechanism for vegetation that enables it to begin photosynthesis rapidly at, or shortly before, the onset of rain [80]. The second GPP peak (smaller shaded area in Figure 6) can be explained by the second, smaller, rainfall event of that year, which was not sufficient enough to replenish PAW to previous levels. However, it created enough reduction in VPD that stimulated the vegetation to resume C assimilation ( Figure 6). Table 3. Summary of the regression analysis between eddy covariance gross primary productivity (EC GPP) and three field-measured water stress controls: plant-available water (PAW), vapor pressure deficit (VPD) and antecedent precipitation index (API) for each site. Also shown are the root-mean-square error (RMSE) and Bayesian information criterion (BIC) for each model.       Relative humidity (RH) begins to increase and vapor pressure deficit (VPD) begins to decrease a full month before the onset of the rainy season. Once the rains fall, plant-available water (PAW) is replenished and GPP begins to increase commencing the greening phase. Although PAW has been gradually decreasing during the growing season, the decrease in rainfall prompts a decrease in RH and an increase in VPD, which sharply reduced GPP due to stomatal closure. All variables have been normalized to between zero and one for visual purposes.

Eddy Covariance Gross Primary Productivity and MODIS-Derived Data
EVI was strongly correlated with EC GPP across all sites (R 2 = 0.83, RMSE = 1.04 g C m −2 d −1 ) ( Table 5). The partial correlation of the MODIS data showed that the EVI was closely coupled with EC GPP during both greening and browning phases ( Table 4). The decline in PAW during the browning phase leads to a reduction in transpiration and latent heat flux and an increase in sensible heat flux and LST (rs = −0.34) (Table 4, Figure 5). MODIS NBAR Band 7 exhibits a positive response during the greening (rs = 0.32) and browning phases (rs = 0.22), probably due to the band's sensitivity to changes in soil moisture during the wetting and drying phases. The relationship between EVI, LST, and MODIS NBAR Band 7 is shown in Figure 7. The slope of the regression line during the dry season (β1 = −0.24) shows a rapid increase in MODIS NBAR Band 7 for each unit decrease in EVI, whereas the change is more gradual during the growing season (Figure 7). Both MODIS NBAR Band 7 (0.20 < Figure 6. A narrowed-down example of a typical Sahelian growing season exemplified here by the 2009 growing season in Demokeya. Relative humidity (RH) begins to increase and vapor pressure deficit (VPD) begins to decrease a full month before the onset of the rainy season. Once the rains fall, plant-available water (PAW) is replenished and GPP begins to increase commencing the greening phase. Although PAW has been gradually decreasing during the growing season, the decrease in rainfall prompts a decrease in RH and an increase in VPD, which sharply reduced GPP due to stomatal closure. All variables have been normalized to between zero and one for visual purposes.

Eddy Covariance Gross Primary Productivity and MODIS-Derived Data
EVI was strongly correlated with EC GPP across all sites (R 2 = 0.83, RMSE = 1.04 g C m −2 d −1 ) ( Table 5). The partial correlation of the MODIS data showed that the EVI was closely coupled with EC GPP during both greening and browning phases ( Table 4). The decline in PAW during the browning phase leads to a reduction in transpiration and latent heat flux and an increase in sensible heat flux and LST (r s = −0.34) (Table 4, Figure 5). MODIS NBAR Band 7 exhibits a positive response during the greening (r s = 0.32) and browning phases (r s = 0.22), probably due to the band's sensitivity to changes in soil moisture during the wetting and drying phases. The relationship between EVI, LST, and MODIS NBAR Band 7 is shown in Figure 7. The slope of the regression line during the dry season (β 1 = −0.24) shows a rapid increase in MODIS NBAR Band 7 for each unit decrease in EVI, whereas the change is more gradual during the growing season (Figure 7). Both MODIS NBAR Band 7 (0.20 < R 2 < 0.50) and LST (0.33 < R 2 < 0.58) had generally moderate relationships with EC GPP. However, when LST and MODIS NBAR Band 7 were included in an MLR model together with EVI, the combination was able to consistently explain higher variance (R 2 ≥ 0.88) across all sites (Figure 8).
Both EVI and MLR GPP follow the seasonal progression of EC GPP well, but the MLR GPP model tracks the dry season EC GPP better than EVI (Figure 9). The inclusion of LST and MODIS NBAR Band 7 improves the variance explained by 6.7% from 0.83 for EVI to 0.89 for the MLR model comprising EVI, LST and MODIS NBAR Band 7 while decreasing the BIC from 1221 to 1024 (Table 5). When the data is split into the individual sites, a similar pattern emerges with the explained variance of MLR model over EVI increasing between 4.3% in Demokeya to 15.9% in Wankama (Table 5). The MLR GPP model for all the sites is shown in Equation (9):   The ability of the MLR model to explain cross-site variability in EC GPP was improved (from 85% to 89%) when data from both the growing and dry seasons were included in the model. Although, there is no green herbaceous vegetation during the dry season, the small C fluxes that were

Conclusions
Hydrological processes generally control vegetation dynamics at multiple spatial and temporal scales. This is particularly true for the Sahel, where the short unimodal rainy season induces a net CO2 uptake that is driven mainly by the herbaceous canopy [13]. Except in highly humid environments, all plants undergo photosynthesis at the expense of losing moisture to the atmosphere. This moisture loss is particularly significant for dryland vegetation, where an imbalance can occur between the amount of water plants require and the limited amount that is available in the ecosystem. In this study, we found that the two main moisture-related biophysical limitations, PAW and VPD together control plant CO2 uptake in the semi-arid conditions. With the start of the dry season in November, low PAW is present in the drying soils of the Sahel, which leads to decreased availability of water for uptake by plant roots (Figures 3 and 4). This, in turn, reduces evapotranspiration (latent heat) due to drier soils and plants close their stomata to prevent moisture loss.
Considering both the importance of drylands in the global C cycle [85] and the dependence of human livelihoods on the products of photosynthesis [8], it is essential to account for water stress controls in order to better model primary productivity in this region. This is particularly important considering the fact that there is a chronic lack of field data on C fluxes in the Sahel. We found that the combination of MODIS NBAR Band 7 as a proxy for soil moisture variability, LST as a proxy for VPD, and EVI as a proxy of photosynthetic activity in an MLR model was able to explain 89% of the variability of EC GPP across the three Sahelian sites (Figures 8 and 9). Since EVI, LST, and MODIS NBAR Band 7 are based on Earth observation data, the MLR model presented here is potentially scalable with repeatable estimates of GPP at relatively high spatial and temporal resolutions. Moreover, the availability of standardized EC flux measurements, such as the recently released FLUXNET2015 database, can potentially eliminate variability in systematic and processing-induced uncertainties between sites. This can further improve model estimates when relating EC GPP with The ability of the MLR model to explain cross-site variability in EC GPP was improved (from 85% to 89%) when data from both the growing and dry seasons were included in the model. Although, there is no green herbaceous vegetation during the dry season, the small C fluxes that were observed could be due to the sparse tree cover [36]. It is reasonable to assume that the dry season signal contains information about land memory effects [81,82]. However, it is unlikely that such effects would be passed on through soil moisture since upper layer dries out within two months of the start of the dry season [69]. Thus, such a memory could be retained in the dormant seeds, roots and foliage [68,83].
The spectral range of MODIS NBAR Band 7 is most sensitive to surface soil water content in general, and the rate of evaporation during the dry season in particular [35]. This is discernible in the relatively rapid increase of the surface reflectance of MODIS NBAR Band 7 compared to the decrease in EVI in response to the decline of the vegetative cover during the dry season (Figure 7). On the other hand, LST is linked to VPD due to the feedback between land (vegetated or bare) and near-surface air [49]. This is clearly shown in the relationship between EVI and LST during both the greening and browning phases in Figure 5. There have been other recent attempts to model GPP in water limited regions using EVI combined with other variables. For example, in a tropical xeric savanna ecosystem, Ma et al. [84] were able to explain 88% of the variability in EC GPP by parameterizing ecosystem light use efficiency using MODIS EVI and top-of-atmosphere photosynthetically active radiation. In another study, Sjöström et al. [21] found that the combination of MODIS EVI with flux tower-derived evaporative fraction, as a proxy of water availability, and photosynthetically active radiation significantly improved the modeling of EC GPP for seven African sites, including Demokeya and Wankama Fallow, with up to 73% of the variance explained. Using only Earth observation data, our model is able to explain 89% of the variance in EC GPP across the three Sahelian sites.

Conclusions
Hydrological processes generally control vegetation dynamics at multiple spatial and temporal scales. This is particularly true for the Sahel, where the short unimodal rainy season induces a net CO 2 uptake that is driven mainly by the herbaceous canopy [13]. Except in highly humid environments, all plants undergo photosynthesis at the expense of losing moisture to the atmosphere. This moisture loss is particularly significant for dryland vegetation, where an imbalance can occur between the amount of water plants require and the limited amount that is available in the ecosystem. In this study, we found that the two main moisture-related biophysical limitations, PAW and VPD together control plant CO 2 uptake in the semi-arid conditions. With the start of the dry season in November, low PAW is present in the drying soils of the Sahel, which leads to decreased availability of water for uptake by plant roots (Figures 3 and 4). This, in turn, reduces evapotranspiration (latent heat) due to drier soils and plants close their stomata to prevent moisture loss.
Considering both the importance of drylands in the global C cycle [85] and the dependence of human livelihoods on the products of photosynthesis [8], it is essential to account for water stress controls in order to better model primary productivity in this region. This is particularly important considering the fact that there is a chronic lack of field data on C fluxes in the Sahel. We found that the combination of MODIS NBAR Band 7 as a proxy for soil moisture variability, LST as a proxy for VPD, and EVI as a proxy of photosynthetic activity in an MLR model was able to explain 89% of the variability of EC GPP across the three Sahelian sites (Figures 8 and 9). Since EVI, LST, and MODIS NBAR Band 7 are based on Earth observation data, the MLR model presented here is potentially scalable with repeatable estimates of GPP at relatively high spatial and temporal resolutions. Moreover, the availability of standardized EC flux measurements, such as the recently released FLUXNET2015 database, can potentially eliminate variability in systematic and processing-induced uncertainties between sites. This can further improve model estimates when relating EC GPP with Earth observation data. Studies of the C cycle often focus on the growing season as it is the principal period where C assimilation takes place, however, the inclusion of dry season dynamics can potentially improve the explanatory capacity of GPP models by accounting for land memory effects. Further evaluation of this approach using more dryland sites from the FLUXNET2015 database as well as other types of in-situ validation data is required to test its efficiency in modeling GPP in water-limited areas.