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

Abstract

Soil CO₂ efflux (F_soil) 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 F_soil 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 F_soil can help evaluate F_soil models for water-limited ecosystems. Here we combine automated soil chamber and flux tower data with models to investigate how soil temperature (T_s), soil moisture (θ), and gross ecosystem photosynthesis (GEP) control F_soil in semiarid ecosystems with similar climates and different vegetation types. Across grassland, shrubland, and savanna sites, θ regulated the relationship between F_soil and T_s, and GEP influenced F_soil magnitude. Thus, the combination of T_s, θ, and GEP controlled rates and patterns of F_soil. In a root exclusion experiment at the grassland, we found that growing season autotrophic respiration accounted for 45% of F_soil. Our modeling results indicate that a combination of T_s, θ, and GEP terms is required to model spatial and temporal dynamics in F_soil, 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 F_soil models can help reduce uncertainty in semiarid ecosystem carbon dynamics.

1. 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 (CO₂) efflux (F_soil) represents CO₂ 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.

2. Materials and Methods

2.1. 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. Description of the study sites.

	Walnut Gulch Kendall Grassland (Grassland)	Lucky Hills Shrubland (Shrubland)	Santa Rita Mesquite Savanna (Savanna)
Year	2017	2012	2015
Latitude, longitude (°)	31.7378° N, 109.9428° W	31.749° N, 110.052° W	31.822° N, 110.867° W
Elevation (m)	1530	1370	1120
Mean air temp. (°C)	15.6	17.6	19.0
Mean annual precip. (1971–2010; mm)	346	320	384
Mean annual GEP (g C m−2 year−1)	227	159	331
Mean LAI (MODIS)	0.30	0.25	0.37
Woody cover (%)	3	40	35
Perennial grass/forb cover (%)	37	3	15
Soil type	Very gravelly, sandy to fine sandy, and clayey loams	Gravelly sandy loams	Deep loamy sands
Plots	Grass (n = 4) Trenched (n = 4)	Shrub (n = 4) Intercanopy (n = 4)	Under tree (n = 2) Intercanopy (n = 3)

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.

2.2. Soil CO₂ Efflux and Environmental Measurements

The net efflux of carbon dioxide (CO₂) 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 CO₂ molar fraction over each 120 s measurement interval. We excluded F_soil estimates from fits with R² < 0.90 and values of F_soil < −1 or >15 µmol CO₂ 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 CO₂ 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, ECH₂O 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 ECH₂O probes, respectively. Importantly, the intercanopy plots at the shrubland and savanna sites were not trenched and therefore were likely influenced by root activity.

2.3. 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.

2.4. 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.

2.5. 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]:

$$F_{soil}=F_{ref}{e}^{b{T}_s},$$

(1)

where F_soil is soil CO₂ efflux (µmol CO₂ m⁻² s⁻¹), F_ref is the basal F_soil when T_s is 0 °C (µmol CO₂ m⁻² s⁻¹), 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:

$$F_{soil}=F_{ref,\theta }{[1-c(\theta -{\theta }_{opt})]}^2{e}^{b{T}_s},$$

(2)

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:

$$F_{soil}=F_{ref,GEP}\frac{\frac{GEP}{GE{P}_{max}}+n}{1+n}{e}^{b{T}_s},$$

(3)

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

$$F_{soil}=F_{ref,\theta ,GEP}\frac{\frac{GEP}{GE{P}_{max}}+n}{1+n}{[1-c(\theta -{\theta }_{opt})]}^2{e}^{b{T}_s},$$

(4)

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 (R²), 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.

3. Results

3.1. Seasonality of Soil CO₂ 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 CO₂ 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 CO₂ 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).

3.2. Environmental Controls on Soil CO₂ 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 CO₂ 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).

3.3. Physiological Controls on Soil CO₂ 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 (R² = 0.66). Daily mean F_soil 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 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).

3.4. 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. Fitted model (Equations (1)–(4)) parameters and the coefficient of determination (R²), Akaike information criterion (AIC), and root mean squared error (RMSE, µmol CO₂ 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 R²; lowest AIC; lowest RMSE).

Site	Plot	Model	Drivers	${\mathit{F}}_{\mathit{r}\mathit{e}\mathit{f}}$	b	c	n	n	R2	AIC	RMSE
Grassland	Grass	1	Ts	0.44	0.04	-	-	244	0.12	568	0.80
	Grass	2	Ts, θ	0.75	0.04	69.38	-	244	0.75	268	0.42
	Grass	3	Ts, GEP	1.10	0.04	-	0.23	244	0.77	252	0.41
	Grass	4	Ts, θ, GEP	0.99	0.04	56.54	0.84	244	0.86	142	0.33
Grassland	Trenched	1	Ts	0.18	0.06	-	-	154	0.37	169	0.42
	Trenched	2	Ts, θ	0.43	0.04	95.93	-	154	0.79	3	0.24
	Trenched	3	Ts, GEP	0.35	0.06	-	0.53	154	0.65	79	0.31
	Trenched	4	Ts, θ, GEP	0.47	0.04	89.34	3.80	154	0.80	−3	0.24
Shrubland	Shrub	1	Ts	0.76	0.00	-	-	164	0.00	293	0.59
	Shrub	2	Ts, θ	2.61	−0.02	103.63	-	164	0.66	119	0.35
	Shrub	3	Ts, GEP	2.11	0.00	-	0.24	164	0.50	182	0.42
	Shrub	4	Ts, θ, GEP	3.02	−0.02	98.56	2.03	164	0.68	108	0.34
	Shrub *	3 *	Ts, GEP *	1.76	0.01	-	0.18	163	0.63	130	0.36
	Shrub *	4 *	Ts, θ, GEP *	3.18	−0.02	96.89	1.25	163	0.74	76	0.31
Savanna	Tree	1	Ts	0.85	0.03	-	-	255	0.05	711	0.98
	Tree	2	Ts, θ	1.42	0.03	55.50	-	255	0.54	526	0.68
	Tree	3	Ts, GEP	2.82	0.01	-	0.18	255	0.41	591	0.77
	Tree	4	Ts, θ, GEP	3.04	0.01	47.92	0.61	255	0.64	466	0.60
	Tree *	3 *	Ts, GEP *	3.07	0.01	-	0.11	253	0.52	532	0.69
	Tree *	4 *	Ts, θ, GEP *	3.18	0.01	44.11	0.41	253	0.69	423	0.56

Models 1–4 have the form of Equations (1)–(4) described in Section 2.5. F_soil is soil CO₂ efflux; θ is volumetric soil moisture; θ_opt is the optimal θ for F_soil; GEP is gross ecosystem photosynthesis; GEP_max is the maximum value of GEP. Each row lists the model parameters (F_ref, b, c, and n). * indicates models in which F_soil was lagged relative to GEP (1 day at shrubland; 2 days at the savanna) based on results from a cross-correlation analysis.

). As shown in Section 3.2 and Section 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 R² lower AIC, and lower RMSE (Table 2). For the grass plots, adding either a moisture or photosynthesis term to Equation (1) increased R² 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. Lag times for maximum cross-correlation between daily means of gross ecosystem photosynthesis (GEP) and soil CO₂ efflux (F_soil). Also shown is the coefficient of determination (R²) of linear regressions between un-lagged and lagged daily mean θ and GEP for the grassland, shrubland, and savanna sites.

Site	Lag (Days)	R2	R2
	GEP-Fsoil	GEP-θ No lag	GEP-θ with lag
Grassland	0	0.53	-
Shrubland	1	0.34	0.47
Savanna	2	0.14	0.26

All regressions significant at p < 0.01.

). 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).

Importantly, model drivers influenced temporal dynamics in predicted F_soil (Figure 6 and Figure 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).

4. 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.

4.1. 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].

4.2. Ecosystem Photosynthesis Stimulates Soil CO₂ 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, Table 2 and Table 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 (Figure 2 and Figure 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 (Figure 3 and Figure 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 (R² = 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.

4.3. 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].

4.4. Vegetation Activity and Structure Influence the Relative Importance of Soil CO₂ 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].

5. 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.