Environmental and Vegetative Controls on Soil CO2 Efflux in Three Semiarid Ecosystems

Soil CO2 efflux (Fsoil) is a major component of the ecosystem carbon balance. Globally expansive semiarid ecosystems have been shown to influence the trend and interannual variability of the terrestrial carbon sink. Modeling Fsoil in water-limited ecosystems remains relatively difficult due to high spatial and temporal variability associated with dynamics in moisture availability and biological activity. Measurements of the processes underlying variability in Fsoil can help evaluate Fsoil models for water-limited ecosystems. Here we combine automated soil chamber and flux tower data with models to investigate how soil temperature (Ts), soil moisture (θ), and gross ecosystem photosynthesis (GEP) control Fsoil in semiarid ecosystems with similar climates and different vegetation types. Across grassland, shrubland, and savanna sites, θ regulated the relationship between Fsoil and Ts, and GEP influenced Fsoil magnitude. Thus, the combination of Ts, θ, and GEP controlled rates and patterns of Fsoil. In a root exclusion experiment at the grassland, we found that growing season autotrophic respiration accounted for 45% of Fsoil. Our modeling results indicate that a combination of Ts, θ, and GEP terms is required to model spatial and temporal dynamics in Fsoil, particularly in deeper-rooted shrublands and savannas where coupling between GEP and shallow θ is weaker than in grasslands. Together, these results highlight that including θ and GEP in Fsoil models can help reduce uncertainty in semiarid ecosystem carbon dynamics.


Introduction
Semiarid ecosystems have been shown to impact global carbon dynamics [1,2]. Ecosystem respiration strongly influences net carbon balance [3] and contributes significantly to variability in the net carbon exchange of semiarid ecosystems [4,5]. Soil carbon dioxide (CO 2 ) efflux (F soil ) represents CO 2 efflux due to belowground plant and microbial respiration and biogeochemical processes, and is a major component of total ecosystem respiration [6,7]. Increased understanding of the processes underlying F soil variation in globally expansive semiarid ecosystems is necessary to reduce uncertainty in terrestrial carbon dynamics.
While controls on respiration processes in more mesic regions are well documented [8,9], F soil in water-limited ecosystems exhibits spatial and temporal variability associated with dynamics in moisture availability and biological activity [10][11][12][13][14][15][16]. Compared to mesic sites, F soil estimates in water-limited ecosystems are more uncertain, partially due to relatively sparse data in drylands despite the recent increase in measurements of F soil globally [17]. Limitations in available data inhibit the development and evaluation of new F soil models for application in water-limited ecosystems. Measurements that examine the processes underlying variability in F soil across a variety of environmental and biological conditions would be useful to develop and evaluate models that recognize the role of temperature, moisture, and substrate limitation on carbon exchange [16,18], particularly in globally extensive drylands projected to expand in response to global change [19,20].
Multivariate models can be useful to represent how dynamics in substrate availability and environmental factors contribute to pulses and seasonality in the metabolic activity of water-limited ecosystems [21][22][23][24]. However, existing biogeochemical models largely represent respiration processes with static temperature sensitivity equations and empirical moisture functions predominantly developed in mesic regions [8,14,25,26]. In water limited-ecosystems, dynamics in soil moisture and photosynthesis strongly regulate F soil over sub-seasonal to interannual timescales [9,27]. Soil moisture availability can influence the magnitude, temperature response, and seasonality of F soil and can cause hysteresis between F soil and its drivers [11,15,16,18,24,[28][29][30][31]. Vegetation structure and function characteristics-including root distribution, hydraulic redistribution, root respiration, photosynthate exudation, and effects on microclimate-can influence the factors that control spatial and temporal variability in F soil [16,22,[32][33][34][35].
Previous studies in water-limited ecosystems have illustrated how F soil varies with interacting environmental and vegetative factors. Variation in plant and soil characteristics modify the response of F soil to changes in water availability and temperature [13,36], and vegetation structure impacts the timescales over which environmental and vegetative factors influence F soil in mixed-vegetation ecosystems [34,37]. Despite advances in our understanding of dryland F soil , representing how these interacting factors impact F soil in heterogeneous ecosystems remains a modeling challenge.
Models are beginning to capture the effects of moisture availability and vegetation activity on the temperature dependency of F soil [31]. Such model structures impose moisture constraints on F soil [38] and assume that respiration processes are stimulated by canopy photosynthesis [39]. However, it is not well known if these new models can capture dynamics in F soil associated with interacting environmental and vegetative factors across structurally diverse semiarid ecosystems.
Multisite measurements targeted to investigate the complex interactions between these drivers can help us determine if new F soil models are broadly applicable in semiarid ecosystems. Trenched-plot experiments can help isolate the interacting effects of environmental and vegetative factors on F soil [6,[40][41][42]. Even if trenched-plots are unavailable, measurements from plots that differ in their distance from patchy vegetation can be used to assess how plants may be influencing F soil through effects on microclimate and root activity [13,34,37].
In this study, we integrated data and modeling to investigate how environmental and vegetative factors influence F soil across three semiarid sites. These sites were similar in climate forcing but differed in stand structure, with major differences in the amounts of grass, shrubs, and trees. The objectives of this study were to (1) combine automated soil chamber and flux tower data to investigate how soil temperature (T s ), soil moisture (θ), and gross ecosystem photosynthesis (GEP) regulate F soil in semiarid grassland, shrubland, and savanna ecosystems; and (2) assess the ability of data-informed models to predict temporal variability in F soil across three structurally diverse semiarid ecosystems. To achieve these objectives, we combined data from a grassland trenched-plot experiment with measurements from intercanopy and under-canopy plots in shrubland and savanna sites that differed in their proximity to vegetation. We then tested model performance at each site to determine if the mechanisms underlying variation in F soil were broadly consistent across these ecosystems. We hypothesize that the combination of T s , θ, and GEP control F soil at each site, and that the relative explanatory value of model drivers varies among sites due to differences in how vegetation structure impacts coupling between shallow soil moisture and carbon exchange. Based on this hypothesis, we predict that the relative explanatory value of θ and GEP will differ the most at sites with deeper rooting depths (savanna > shrubland > grassland) where GEP is less coupled to shallow soil moisture.

Site Description
This study was conducted at three AmeriFlux sites in southeast Arizona, USA. Kendall Grassland (grassland; AmeriFlux site ID: US-Wkg) is a warm-season, semiarid grassland dominated by perennial bunchgrasses (mainly, Eragrostis lehmannia). Lucky Hills Shrubland (shrubland; site ID: US-Whs) is a shrubland composed of a variety of Chihuahuan desert shrubs (Larrea tridentata, Parthenium incanum, Acacia constricta). Both sites are located within the USDA Agricultural Research Service Walnut Gulch Experimental Watershed. Santa Rita Mesquite Savanna (savanna; site ID: US-SRM) is a semiarid grassland that has experienced encroachment by velvet mesquite trees (Prosopis velutina). The savanna site is located in the Santa Rita Experimental Range, roughly 80 km west of the other sites. A detailed description of the sites can be found in a previous study [43]. The sites experience similar mean annual temperature (~17 • C) and mean annual precipitation (320-384 mm) but differ in their vegetative structure and productivity (Table 1 and Figure 1). Grass covers 37% of the grassland, whereas woody cover dominates the shrubland (40%) and savanna (35%). Canopy height and mean annual leaf area index increase from lowest to highest for the shrubland, grassland, and savanna. Roughly 60% of annual precipitation occurs in July-September, associated with the North American Monsoon.

Site Description
This study was conducted at three AmeriFlux sites in southeast Arizona, USA. Kendall Grassland (grassland; AmeriFlux site ID: US-Wkg) is a warm-season, semiarid grassland dominated by perennial bunchgrasses (mainly, Eragrostis lehmannia). Lucky Hills Shrubland (shrubland; site ID: US-Whs) is a shrubland composed of a variety of Chihuahuan desert shrubs (Larrea tridentata, Parthenium incanum, Acacia constricta). Both sites are located within the USDA Agricultural Research Service Walnut Gulch Experimental Watershed. Santa Rita Mesquite Savanna (savanna; site ID: US-SRM) is a semiarid grassland that has experienced encroachment by velvet mesquite trees (Prosopis velutina). The savanna site is located in the Santa Rita Experimental Range, roughly 80 km west of the other sites. A detailed description of the sites can be found in a previous study [43]. The sites experience similar mean annual temperature (~17 °C) and mean annual precipitation (320-384 mm) but differ in their vegetative structure and productivity (Table 1 and Figure 1). Grass covers 37% of the grassland, whereas woody cover dominates the shrubland (40%) and savanna (35%). Canopy height and mean annual leaf area index increase from lowest to highest for the shrubland, grassland, and savanna. Roughly 60% of annual precipitation occurs in July-September, associated with the North American Monsoon.

Soil CO 2 Efflux and Environmental Measurements
The net efflux of carbon dioxide (CO 2 ) at the soil-atmosphere interface (F soil ) was measured using an infrared gas analyzer coupled with automated soil chambers (LI-8100, LI-COR, Lincoln, NE, USA). Automated chambers were deployed at each site in plots near vegetation. Soil collars were inserted to a depth of 8-9 cm, leaving 2-3 cm of the collars exposed. We used the FV8100 Data File Viewer (LI-COR) to estimate F soil by fitting an exponential regression to the rate of increase in CO 2 molar fraction over each 120 s measurement interval. We excluded F soil estimates from fits with R 2 < 0.90 and values of F soil < −1 or >15 µmol CO 2 m −2 s −1 .
In 2017, F soil was measured twice per hour at the grassland using four chambers adjacent to patches of perennial bunchgrass (Eragrostis lehmanniana, "grass"). To exclude the effects of vegetation activity on F soil , we added four additional chambers in bare plots and trenched each plot's perimeter on 22 June 2017 prior to the summer rainy season, hereafter referred to as "trenched". Trenches were dug to~30 cm depth and lined with ground cover fabric to prevent root growth back into the plot. Roughly~84% of the grass roots at this site are within the top 30 cm of soil [44]. We regularly weeded the trenched plots to ensure the soil was bare throughout the growing season. We assume CO 2 efflux measured in trenched plots represents heterotrophic respiration (R h ), while total F soil measured in grass plots includes R h and belowground autotrophic respiration (R a ). We define R a as the difference between grass F soil and trenched R h . Supplementary measurements of T s and θ were measured at a depth of 5 cm with a LI-COR temperature probe and a soil moisture probe (EC-5, Decagon, now METER Group, Washington, DC, USA), respectively. Beginning in June 2017, ECH 2 O 5TM probes (METER Group) were used to measure 5 cm T s and θ for all chambers at the site.
To extend our investigation across sites with differing vegetation structure, we also measured F soil , T s , and θ in the shrubland and savanna. In the shrubland in 2012, F soil was measured every two hours using four chambers under creosote bush shrubs (Larrea tridentata) and four chambers located between the sparsely separated shrubs (~2 m from canopy drip lines). In the savanna in 2015, hourly F soil was measured using three chambers installed halfway between the tree bole and drip line of velvet mesquite trees (Prosopis velutina) and from three chambers~5 m from trees in the intercanopy space. A malfunctioning chamber at the savanna site was excluded from analysis, which reduced the number of tree plots to two. We measured 5 cm T s and θ at the shrubland and savanna using LI-COR temperature probes and ECH 2 O probes, respectively. Importantly, the intercanopy plots at the shrubland and savanna sites were not trenched and therefore were likely influenced by root activity.

Ecosystem Photosynthesis
To quantify how vegetation activity influences F soil , ecosystem-scale carbon fluxes were measured using the eddy covariance technique. Details of the instrumentation and methods used at each site have been described previously [45]. Briefly, 30 min average net ecosystem exchange of CO2 (NEE) was partitioned into gross ecosystem photosynthesis (GEP; hereafter referred to as photosynthesis) and ecosystem respiration (R eco ; [43]). An exponential function was fit to friction velocity-filtered nighttime NEE and air temperature over a~5 day moving window to determine R eco [46]. GEP was calculated as the difference between R eco and NEE, with the sign convention of positive values for GEP and R eco . A previous comparison of R eco and F soil at the savanna site [47] showed that integrated F soil was greater than R eco over the course of a growing season. This indicates that F soil is systematically overestimated, or R eco is underestimated, as R eco should also account for aboveground respiration. If R eco is underestimated, this would result in an underestimate of GEP. However, this systematic bias should not have a large impact on our modeling results so long as GEP and F soil capture the temporal variability in these processes. This is because the empirical model coefficients described below are optimized to fit the data.

Data Analysis
At each site, plot means were calculated as the average of replicates. Missing data and outliers were replaced with the mean of replicates. Hourly means were used to examine the impact of θ on the relationship between F soil and T s . To investigate how water availability influenced the temperature response of F soil at the grassland, we fit Equation (1) to data binned by θ quantiles in 10% increments.
Daily means were calculated from sub-daily measurements to account for differences in sampling rates among sites. The response of F soil to recent carbon inputs was determined by regressing daily mean F soil against daily mean GEP, and we used the Student's t-test to evaluate differences in regression parameters [48]. Daily means were used to investigate seasonality in carbon fluxes and environmental variables and to examine relationships between F soil and GEP. We used the paired t-test to test for differences in daily mean F soil and drivers between plots that varied in their distance from vegetation.
At the grassland, we tested for differences between plots in the basal rate and temperature sensitivity of F soil by testing for overlap in the 95% confidence intervals of coefficients determined by fitting Equation (1) described below.

Model Development
We used a modeling framework to investigate how the inclusion of environmental and vegetative terms influenced predicted spatial and temporal variation in F soil . All models were based on an exponential temperature function [8]: where , and b is the temperature sensitivity of F soil . We supplemented temperature-based models with θ and GEP terms to represent the effects of moisture availability and vegetation activity on F soil [31]. Moisture effects were incorporated into Equation (1) using a quadratic structure that reflects how excessively high or low θ suppresses F soil [38,49,50] as: where θ opt is the optimum θ value for which F soil is greatest and c represents the sensitivity of F soil to θ by controlling the slope of the exponential curve (higher values of c indicate stronger effects of θ). At each site we determined θ opt by examining the response of daily mean F soil to θ and visually estimating the value of θ associated with maximum F soil . Following reference [31], we added a photosynthesis term to Equation (1) to represent the effects of T s and GEP on F soil using: where n represents the degree to which GEP drives F soil relative to heterotrophic processes (n = 0 indicates strong GEP effect on F soil ) and GEP max is the maximum value of GEP. The combined effects of temperature, moisture, and photosynthesis were represented by Models were fit using nonlinear least squares regression in which the coefficients were estimated using an iterative method based on starting values in Matlab (Mathworks, Inc., Natick, MA, USA).
To account for differences in model complexity, model performance was assessed using the coefficient of determination (R 2 ), Akaike Information Criterion (AIC; [51]), and root mean squared error (RMSE). We used cross-correlation to test for lags between daily mean F soil and daily mean GEP. For sites with significant lag, we re-fit Equations (3) and (4) with optimum lag and assessed changes in model performance.

Seasonality of Soil CO 2 Efflux
Across all sites, daily mean F soil and GEP followed seasonal dynamics of changes in water availability (Figure 2a,c,d; Figures S1 and S2). At the grassland site with grass and trenched plots, a brief and limited spring growing season (DOY 75-100) was followed by low F soil , GEP, and θ, despite increasing T s (Figure 2a-d). Average pre-summer monsoon (DOY 0-175) daily mean F soil for the grass plot was 0.52 µmol CO 2 m −2 s −1 . During the monsoon (DOY 175-250), θ was high and average daily mean F soil for the grass plot increased significantly to an average 2.3 µmol CO 2 m −2 s −1 (p < 0.01). Rates of GEP responded gradually to the onset of monsoon precipitation, whereas F soil increased rapidly with θ. (Figure 2a,c,d). Post-monsoon (DOY 250-365) rates of F soil and GEP decreased following seasonal decreases in GEP, θ and T s (Figure 2a-d).

Environmental Controls on Soil CO2 Efflux
Median Fsoil increased with θ ( Figures S3-S5), and daily mean θ contributed to 51-77% of the variation in daily mean Fsoil at all sites. (Figure S6-S8). Ts explained significant variation in Fsoil for high θ, but Ts and Fsoil were weakly coupled when θ was low (Figure 3a). Since the amount of variation in Fsoil explained by Equation (1) varied significantly with θ, we used the quantile fit results ( Figure  3a) and re-fit Equation (1) into wet (grass: θ > 7th quantile; trenched: θ > 6th quantile) and dry (grass: θ < 8th quantile; trenched: θ < 7th quantile) conditions. Rates of Fsoil were generally low for dry conditions, despite increasing Ts, whereas Fsoil increased strongly with Ts when the soil was wet (Figure 3b,c). Basal soil CO2 efflux (Fref) and the temperature sensitivity of Fsoil (b) varied significantly with θ and differed between the grass and trenched plots (Figure 3b,c; p < 0.01). Fref was 54% and 64%

Environmental Controls on Soil CO 2 Efflux
Median F soil increased with θ ( Figures S3-S5), and daily mean θ contributed to 51-77% of the variation in daily mean F soil at all sites. (Figures S6-S8). T s explained significant variation in F soil for high θ, but T s and F soil were weakly coupled when θ was low (Figure 3a). Since the amount of variation in F soil explained by Equation (1) varied significantly with θ, we used the quantile fit results ( Figure 3a) and re-fit Equation (1) into wet (grass: θ > 7th quantile; trenched: θ > 6th quantile) and dry (grass: θ < 8th quantile; trenched: θ < 7th quantile) conditions. Rates of F soil were generally low for dry conditions, despite increasing T s , whereas F soil increased strongly with T s when the soil was wet (Figure 3b,c). Basal soil CO 2 efflux (F ref ) and the temperature sensitivity of F soil (b) varied significantly with θ and differed between the grass and trenched plots (Figure 3b,c; p < 0.01). F ref was 54% and 64% greater for wet than dry conditions at the grass and trenched plots, respectively. Between plots, grass F ref was 63% and 73% greater than trenched F ref for wet and dry conditions, respectively. Wet conditions were associated with greater b than dry conditions, and this difference was more pronounced in vegetated plots than in trenched ones. Similar to the grassland, wet conditions at the savanna corresponded with high F ref and b; however, the temperature response of F soil at the savanna was more variable than at the grassland ( Figure S9). Unexpectedly, F soil did not show a clear response to T s at the shrubland ( Figure S10). For all sites, we found that T s alone was not the only driver of F soil and that even when accounting for variation in θ, significant variation in F soil remained unexplained (Figure 3, Figures S9 and S10). greater for wet than dry conditions at the grass and trenched plots, respectively. Between plots, grass Fref was 63% and 73% greater than trenched Fref for wet and dry conditions, respectively. Wet conditions were associated with greater b than dry conditions, and this difference was more pronounced in vegetated plots than in trenched ones. Similar to the grassland, wet conditions at the savanna corresponded with high Fref and b; however, the temperature response of Fsoil at the savanna was more variable than at the grassland ( Figure S9). Unexpectedly, Fsoil did not show a clear response to Ts at the shrubland ( Figure S10). For all sites, we found that Ts alone was not the only driver of Fsoil and that even when accounting for variation in θ, significant variation in Fsoil remained unexplained (Figures 3, S9 and S10).

Physiological Controls on Soil CO2 Efflux
Although the seasonal pattern of Fsoil at the grassland was similar for the grass and trenched plots, there were significant differences in the magnitude of daily mean Fsoil between plots (Figure 2a) that strongly correlated with daily mean GEP (R 2 = 0.66). Daily mean Fsoil during the monsoon was significantly greater for the grass (2.3 µmol CO2 m −2 s −1 ) than trenched plots (1.2 µmol CO2 m −2 s −1 ; p < 0.01), despite similar Ts and θ (p > 0.1). Using the difference in Fsoil between grass and trenched plots

Physiological Controls on Soil CO 2 Efflux
Although the seasonal pattern of F soil at the grassland was similar for the grass and trenched plots, there were significant differences in the magnitude of daily mean F soil between plots (Figure 2a) that strongly correlated with daily mean GEP (R 2 = 0.66). Daily mean F soil during the monsoon was significantly greater for the grass (2.3 µmol CO 2 m −2 s −1 ) than trenched plots (1.2 µmol CO 2 m −2 s −1 ; p < 0.01), despite similar T s and θ (p > 0.1). Using the difference in F soil between grass and trenched plots in the grassland, we estimate that belowground autotrophic (R a ) and heterotrophic (R h ) respiration accounted for 44% and 56% of cumulative growing season F soil , respectively (Figure 4).
To investigate how plant activity influenced F soil across sites with varying vegetation type and productivity, we examined the relationship between F soil and GEP. Daily mean F soil increased with daily mean GEP at all sites, and the rate of increase was greater for plots near vegetation ( Figure 5; p < 0.01). At all sites, F soil was 35-59% greater for plots near vegetation compared to plots that were either trenched (grassland only) or located further from vegetation (~2-5 m). in the grassland, we estimate that belowground autotrophic (Ra) and heterotrophic (Rh) respiration accounted for 44% and 56% of cumulative growing season Fsoil, respectively ( Figure 4). To investigate how plant activity influenced Fsoil across sites with varying vegetation type and productivity, we examined the relationship between Fsoil and GEP. Daily mean Fsoil increased with daily mean GEP at all sites, and the rate of increase was greater for plots near vegetation ( Figure 5; p < 0.01). At all sites, Fsoil was 35-59% greater for plots near vegetation compared to plots that were either trenched (grassland only) or located further from vegetation (~2-5 m).   in the grassland, we estimate that belowground autotrophic (Ra) and heterotrophic (Rh) respiration accounted for 44% and 56% of cumulative growing season Fsoil, respectively ( Figure 4). To investigate how plant activity influenced Fsoil across sites with varying vegetation type and productivity, we examined the relationship between Fsoil and GEP. Daily mean Fsoil increased with daily mean GEP at all sites, and the rate of increase was greater for plots near vegetation ( Figure 5; p < 0.01). At all sites, Fsoil was 35-59% greater for plots near vegetation compared to plots that were either trenched (grassland only) or located further from vegetation (~2-5 m).

Model Performance
To integrate these varied environmental controls on F soil we used a multivariate modeling approach by sequentially adding T s , θ, and GEP as explanatory variables. For the grassland, we tested the ability of data-informed models to predict temporal variability in F soil . The model based solely on T s (Equation (1)) explained less than 40% of the variation in observed daily mean F soil for the grass and trenched plots ( Table 2). As shown in Sections 3.2 and 3.3, the temperature response of F soil varied strongly with θ and the magnitude of F soil was related to GEP. Models that represented these observed effects of θ (Equation (2)) and GEP (Equation (3)) on F soil outperformed Equation (1), as indicated by higher R 2 lower AIC, and lower RMSE ( Table 2). For the grass plots, adding either a moisture or photosynthesis term to Equation (1) increased R 2 to a similar degree. Conversely, in the trenched plots that were manipulated to exclude root activity associated with photosynthesis, goodness of fit metrics show that the model with a moisture term (Equation (2)) was better than the model with a photosynthesis term (Equation (3)). The complete model-which included temperature, moisture, and photosynthesis terms (Equation (4))-outperformed less complex models in the grass plots. However, in the trenched plots that were uninfluenced by GEP, Equations (2) and (4) explained a similar amount of variation in F soil but Equation (4) had lower AIC.
We also tested the models at the shrubland and savanna to determine if the trend in performance was consistent across sites with different vegetation. As in the grassland, temperature alone was a poor predictor of variation in F soil , and adding moisture (Equation (2)) or photosynthesis (Equation (3)) terms strongly improved model performance ( Table 2). Adding a moisture term to the temperature-based model explained more variation in F soil than did adding a photosynthesis term (Table 2). To test if this difference in relative explanatory power was related to the timing of photosynthesis relative to microbial respiration of root exudates, we used cross-correlation analysis to investigate lags between F soil and GEP. Correlation was maximized when F soil was lagged relative to GEP by zero days in the grassland, one day in the shrubland, and two days in the savanna (Table 3). Applying these lags and re-fitting the models increased the amount of variation in F soil explained by Equation (3) to be comparable to Equation (2) at the shrubland and savanna. The complete model (Equation (4)) performed best in the shrubland and savanna. As indicated by lower AIC, Equation (4) improved model performance most in the savanna-which is also where we observed the weakest coupling between daily mean GEP and θ and the largest F soil -GEP lag among sites (Table 3). We found that the relative explanatory value of model drivers varied among sites (Table 2). Table 2. Fitted model (Equations (1)-(4)) parameters and the coefficient of determination (R 2 ), Akaike information criterion (AIC), and root mean squared error (RMSE, µmol CO 2 m −2 s −1 ) used to assess model performance at the grassland, shrubland, and savanna sites. Bold numbers indicate best performance among model groups (highest R 2 ; lowest AIC; lowest RMSE).  Table 3. Lag times for maximum cross-correlation between daily means of gross ecosystem photosynthesis (GEP) and soil CO 2 efflux (F soil ). Also shown is the coefficient of determination (R 2 ) of linear regressions between un-lagged and lagged daily mean θ and GEP for the grassland, shrubland, and savanna sites. Importantly, model drivers influenced temporal dynamics in predicted F soil (Figures 6 and 7). Equation (1) (T s ) failed to reproduce the seasonality observed in F soil , generally over-predicting F soil during the dry pre-monsoon period and under-predicting F soil during the growing season ( Figure 6, Figures S11 and S12). Adding a moisture term to the temperature-based model improved predicted seasonality in F soil because it better captured variability in observed F soil and predicted high F soil immediately following rain events at the monsoon onset. However, Equation (2) tended to underestimate growing season F soil since it did not represent the stimulating effect of GEP on F soil (Figure 4). Adding a photosynthesis term (Equation (3)) better predicted the magnitude of growing season F soil but was delayed relative to observations due to lags between the onset of high θ and GEP upregulation. Thus, the inclusion of both moisture and photosynthesis terms in Equation (4) was required to model the seasonality, magnitude, and variability in F soil at all sites (Figure 7). Table 3. Lag times for maximum cross-correlation between daily means of gross ecosystem photosynthesis (GEP) and soil CO2 efflux (Fsoil). Also shown is the coefficient of determination (R 2 ) of linear regressions between un-lagged and lagged daily mean θ and GEP for the grassland, shrubland, and savanna sites.

Site
Lag ( Importantly, model drivers influenced temporal dynamics in predicted Fsoil (Figures 6 and 7). Equation (1) (Ts) failed to reproduce the seasonality observed in Fsoil, generally over-predicting Fsoil during the dry pre-monsoon period and under-predicting Fsoil during the growing season (Figures 6, S11 and S12). Adding a moisture term to the temperature-based model improved predicted seasonality in Fsoil because it better captured variability in observed Fsoil and predicted high Fsoil immediately following rain events at the monsoon onset. However, Equation (2) tended to underestimate growing season Fsoil since it did not represent the stimulating effect of GEP on Fsoil (Figure 4). Adding a photosynthesis term (Equation (3)) better predicted the magnitude of growing season Fsoil but was delayed relative to observations due to lags between the onset of high θ and GEP upregulation. Thus, the inclusion of both moisture and photosynthesis terms in Equation (4) was required to model the seasonality, magnitude, and variability in Fsoil at all sites (Figure 7).

Discussion
In three semiarid ecosystems we found that Ts, θ, and GEP influenced the dynamics, magnitude, and variability of Fsoil. Water availability strongly influenced Fsoil rates and patterns, whereas GEP stimulated Fsoil, particularly for plots near vegetation. These results provide additional evidence that moisture availability regulates temporal variation in Fsoil, and biological factors impact spatial variation in Fsoil [10,11,13,52]. The complete model (Equation (4)) integrated Ts, θ, and GEP controls and better captured temporal dynamics in observed Fsoil than less complex models. Testing the model across sites with similar climate forcing indicated that the explanatory value of model drivers varied with vegetation structure and productivity. Together, these results show that models that account for Ts, θ, and GEP can represent how Fsoil responds to changes in water availability and vegetation activity in ecosystems with varying structure.

Discussion
In three semiarid ecosystems we found that T s , θ, and GEP influenced the dynamics, magnitude, and variability of F soil . Water availability strongly influenced F soil rates and patterns, whereas GEP stimulated F soil , particularly for plots near vegetation. These results provide additional evidence that moisture availability regulates temporal variation in F soil , and biological factors impact spatial variation in F soil [10,11,13,52]. The complete model (Equation (4)) integrated T s , θ, and GEP controls and better captured temporal dynamics in observed F soil than less complex models. Testing the model across sites with similar climate forcing indicated that the explanatory value of model drivers varied with vegetation structure and productivity. Together, these results show that models that account for T s , θ, and GEP can represent how F soil responds to changes in water availability and vegetation activity in ecosystems with varying structure.

Water Availability Limits Autotrophic and Heterotrophic Respiration
The temperature response of F soil was conditional on θ ( Figure 3). Modeling these interactions is important since warming-driven reductions in θ can suppress F soil despite higher T s [23]. In the grassland, high θ enhanced the temperature sensitivity of F soil , whereas low θ suppressed F soil in the grass and trenched plots (Figure 3), which indicates that water availability constrains both R a and R h . Low soil moisture can inhibit R h by decreasing substrate availability, microbial activity, solute transport, or some combination of these drivers [23,29,53,54]. Moisture limitation may also suppress R a through reductions in root exudates due to decreased rates of photosynthesis and phloem transport in water-stressed plants [23,55]. Thus, changes in moisture availability can cause seasonal variation in the magnitude and temperature response of F soil in semiarid ecosystems, as previously found in mesic forests [38]. Models that account for interactions between T s and θ are more apt to capture seasonality and pulsed dynamics in F soil that impact the carbon balance of semiarid ecosystems [7,56]. The need to represent water stress effects on F soil is likely to apply beyond semiarid ecosystems since most regions already experience periods of water limitation [57] and drylands are projected to expand [19].

Ecosystem Photosynthesis Stimulates Soil CO 2 Efflux
The link between GEP and F soil contributes to spatial variation in F soil rates ( Figure 5). We found that recent photosynthesis impacts F soil likely through enhanced root respiration and the stimulating effect of root exudation on microbial respiration ( Figure 5, Tables 2 and 3), which has been reported across a variety of ecosystems [11,35,37,39,58]. Even when θ was similar, growing season rates of F soil were greater for plots near vegetation (Figures 2 and 3). Even though the shrubland and savanna did not have trenched plots, F soil closer to the vegetation was higher and responded more strongly to photosynthesis variation. Despite the uncertainty in GEP due to NEE measurement and partitioning bias, and differences in measurement scale, GEP was correlated with F soil and was important to predict temporal dynamics in F soil (Table 3; [13]). Note that since GEP used here is an ecosystem-scale flux, and photosynthetic inputs are likely to vary across space (Figures 3 and 4), predictive models of F soil could be improved if new tools to disaggregate ecosystem flux measurements were used to determine the spatial distribution of GEP [59].
The effects of GEP on F soil are illustrated by seasonal changes in F soil partitioning. We found that the difference in F soil between plots increased as the growing season progressed (Figure 2, Figures S1 and S2), and F soil was greater and more sensitive to GEP for plots near vegetation ( Figure 5), as previously reported in this region [13]. These dynamics are likely linked to plant physiology and phenology, which have been shown to affect the magnitude and partitioning of F soil in temperate forests [41,60] and California grasslands [11]. Applying the model at the grassland showed that GEP had a stronger effect on F soil for the grass plots (Table 2; low n: strong GEP effect on F soil ) than the trenched plots (high n: weak GEP effect on F soil ). At the grassland, our estimate of R a (difference in F soil between the grass and trenched plots) correlated strongly with GEP (R 2 = 0.66) and was a considerable fraction (44%) of total growing season F soil (Figure 4). While we did not have trenched plots at the shrubland and savanna to partition F soil , differences in the seasonal pattern of F soil for plots that differed in their proximity to vegetation indicate that R a is likely also a considerable fraction of F soil at these sites ( Figure 5, Figures S1 and S2). Our estimate of the growing season R a :F soil ratio for the grassland is lower than the mean value reported in a review of grass and crop ecosystems (60.4%; [61]) but similar to results from a mesic grassland (48-52%; [62]). Since R a can be a significant component of F soil in ecosystems that span a wide range of water availability, refined understanding of controls on R a is necessary to reduce uncertainty in F soil .

Moisture and Photosynthesis Terms Improve Modeled Carbon-Water Dynamics
Model predictions based solely on temperature do not accurately reflect F soil in water-limited ecosystems. However, by explicitly representing the combined effects of T s , θ, and GEP, the full model (Equation (4)) predicted temporal variation in observed F soil associated with dynamics in moisture availability and vegetation activity across structurally diverse sites (Figure 7). At the shrubland in particular, Equation (4) explained 74% of the variation in daily mean F soil even though we did not observe a relationship between F soil and T s ( Table 2). Decoupling between F soil and T s when moisture was limiting (Figure 3) likely explains why the temperature-only model (Equation (1)) did not capture seasonal dynamics in F soil (Figure 6). By adding θ to a temperature-based model, predicted F soil was suppressed when water was limiting and enhanced when θ was optimal ( Figure 6). Together, T s and θ explained more than 50% of the observed variability across sites ( Table 2). The superior performance of Equation (2) over Equations (1) and (3) across sites with different vegetation structure underscores that water availability is a key control on respiration processes in semiarid ecosystems (Table 2).
While supplementing a temperature-based model with either θ or GEP terms increased the amount of explained variation in F soil to a similar degree, the combination of T s , θ, and GEP was required to maximize model performance and predict seasonality in F soil . Models that accounted for θ captured the pulsed increase in metabolic activity at the monsoon onset characteristic of semiarid ecosystems [12,21,63], whereas GEP terms improved the prediction of F soil magnitude and seasonality by reflecting the stimulating effect of photosynthesis on basal F soil ([39]; Figure 6). We found that F soil increased rapidly in response to increased θ at the beginning of the monsoon, whereas GEP increased more gradually (Figure 2), which reflect differences in the timing of ecosystem responses to rainfall pulses [56]. While these results indicate that this model captures F soil dynamics in these subtropical, warm-season ecosystems, future studies should test this model in cool-season desert ecosystems. We also found that predictions from GEP-based models lagged observed F soil . Previous research has documented lags between GEP and F soil ranging from hourly to daily timescales depending on the vegetative cover and time of year [22,31,37,64]. Consistent with previous research, no lag was detected at the grassland [65]. However, applying one or two days of lag between GEP and F soil improved model performance at the shrubland and savanna (Table 2). These results provide additional evidence in support of incorporating lag information in semi-empirical F soil models [65]. Together, our findings indicate that models with T s , θ, and GEP terms can better capture rainfall-driven pulses in carbon dynamics than simpler models [56].

Vegetation Activity and Structure Influence the Relative Importance of Soil CO 2 Efflux Drivers
The degree of vegetation activity influences the relative importance of F soil controls. In the grassland, F soil for grass plots was more sensitive to GEP (Table 2; low n), whereas F soil for trenched plots was more sensitive to θ (high c). This result is consistent with our expectation that θ would more strongly regulate F soil from plots manipulated to exclude the effects of GEP on belowground activity. Similarly, F soil was more sensitive to θ than GEP (Table 2; high c, high n) at sites with low cumulative GEP (shrubland, grassland trenched plots). We observed unexpected differences between sites in how θ influenced the relationship between F soil and T s . Contrary to the grassland, the effect of θ on the relationship between F soil and T s was weaker in the savanna and was not observed in the shrubland (Figure 3, Figures S9 and S10). Previous work in this region found that the temperature sensitivity of F soil was lower during wet conditions in grass plots but not influenced by moisture in plots near mesquite trees [37]. The complete model captured how vegetation modulated the effects of environmental controls on F soil and therefore may be applicable in various ecosystems subject to water limitation.
Interactions between vegetation structure and carbon-water coupling can help explain site differences in the explanatory power of F soil controls. Vegetation can cause decoupling and lags between F soil and its controls [16,34] due to plant structure and rooting characteristics. Previous work in this region found that F soil was more sensitive to antecedent photosynthesis rates in mesquite plots, whereas F soil near grass plots was more influenced by same-day photosynthesis [37]. Similarly, we found greater lag between GEP and F soil (Table 3) at the savanna (two days) and shrubland (one day) than the grassland (zero days), perhaps due to larger structure and longer phloem transport distance for the woody plants [22,37]. While θ and GEP controls were interchangeable for the grass plots, θ had greater explanatory power than unlagged GEP in the shrubland and savanna. Lagging GEP made its explanatory power comparable to θ (Table 2). Thus, we suggest that future semi-empirical models include terms that account for lag. Differences in lags may be related to variation in rooting characteristics between sites. In the short-rooted grassland, strong coupling between shallow θ and GEP leads to covariation which makes either term suitable to explain variation in F soil . Conversely, trees and shrubs generally have a higher proportion of roots in deep soil than grasses [44], and GEP is more coupled to deeper θ [4,64], leading to more of a disconnect between GEP and shallow θ and their effects on F soil [32,56,66].
F soil drivers suggest that ecosystem composition likely alters the magnitude and spatial variability of F soil . Woody encroachment has been shown to increase F soil variation in semiarid grassland [13] and savanna ecosystems [34]. Vegetation structure and functioning contributes to spatial variation in F soil ( Figure 5) and modifies the response of F soil to environmental controls ( Figure 3 and Table 2). The strong performance of the complete model across ecosystems with a differing structure indicates that simple models with environmental and vegetative controls [31] may be useful to investigate how changes in ecosystem composition will impact F soil . To increase the utility of this model, further research should focus on how to represent differences in θ-GEP coupling between woody ecosystems and grasslands [67].

Conclusions
Temperature, moisture, and photosynthesis were each important controls on F soil in grassland, shrubland, and savanna ecosystems. While models relying on T s erroneously predicted high F soil before the growing season, those with θ and GEP controls captured variation in F soil associated with dynamics in moisture availability and vegetation activity. This study is novel in that it is the first to test if a F soil model driven by daily T s , θ, and GEP can capture temporal dynamics and variability in F soil across semiarid sites with similar climate forcing but differing vegetation structure. While the mechanism governing the relative importance of T s , θ, and GEP controls across sites remains unclear, it is likely related to vegetation characteristics associated with productivity and water use. Our results indicate that this simple model structure can capture F soil dynamics associated with transitions from process-rate limitation to substrate constraints [22]. This study builds upon recent modeling advances [31] and indicates that this type of modeling approach can capture spatial and temporal variation in F soil across structurally diverse, semiarid ecosystems, particularly if time series data of plant function is available. Combining this modeling approach with increased monitoring of F soil at flux tower sites could help investigate connections between plot and ecosystem-scale carbon exchange [47]. Future studies should test this model in cool-season ecosystems, which tend to be temperature-limited when soil moisture is non-limiting [24]. It is reasonable to infer that the relative importance of model drivers would differ between cool-season ecosystems and the warm-season ecosystems examined herein. Accounting for the interactive effects of T s , θ, and GEP on F soil will be important to determine the response of water-limited ecosystems to changes in climate and land cover.

Supplementary Materials:
The following are available online: http://www.mdpi.com/2571-8789/3/1/6/s1. Figure S1: Time series of carbon fluxes and controls at the shrubland, Figure S2: Time series of carbon fluxes and controls at the savanna, Figure S3: Relationship between soil moisture and soil CO 2 efflux at the grassland, Figure S4: Relationship between soil moisture and soil CO 2 efflux at the shrubland, Figure S5: Relationship between soil moisture and soil CO 2 efflux at the savanna, Figure S6: Controls on soil CO 2 efflux at the grassland, Figure S7: Controls on soil CO 2 efflux at the shrubland, Figure S8: Controls on soil CO 2 efflux at the savanna, Figure S9: Temperature response of soil CO 2 efflux at the savanna, Figure S10: Temperature response of soil CO 2 efflux at the shrubland, Figure S11: Predicted temporal dynamics of soil CO 2 efflux at the shrubland, Figure S12: Predicted temporal dynamics of soil CO 2 efflux at the savanna.