Introduction

While arid and semiarid (dryland) ecosystems cover a substantial fraction of the terrestrial earth surface (41–47 %) (Reynolds et al. 2007; Schimel 2010) and maintain soils that store nearly twice as much organic carbon (C) as soils in temperate forests (Lal 2004), on a per-unit-area basis dryland ecosystems generally have low productivity and low soil C storage. Perhaps due to the perception of low C density and flux, drylands have been often overlooked as an important source or sink of CO2. Yet the potential magnitude of the dryland C sink is a matter of significant debate (Rotenberg and Yakir 2010; Schlesinger et al. 2009; Wohlfahrt et al. 2008) and emerging evidence suggests that, at the global scale, both inter-annual variability (Poulter et al. 2014) and the overall trend (Ahlström et al. 2015) of the entire land C sink are dominated by drylands. Because dryland ecosystems exhibit high C turnover rates that are closely coupled to variable temperature and precipitation regimes, the dryland C cycle may respond dynamically to ongoing climate change. Indeed, recent evidence of the importance of drylands in global C variability and trends is based upon this dynamism (Poulter et al. 2014; Ahlström et al. 2015).

At the global-scale, soils store more C than the atmosphere and aboveground plant biomass combined, and the flux of CO2 from soil to the atmosphere is one of Earth’s largest. CO2 effluxes from root, biological soil crust, and heterotrophic respiration belowground (which sum to soil respiration, here R s ) are a principle pathway of C loss from terrestrial ecosystems (Luo and Zhou 2010). Thus, testing and improving the current quantitative and predictive frameworks for soil C modeling in drylands is critical for improving future projections of biosphere–atmosphere C exchange. Further, soil C cycling in dry shrublands is highly heterogeneous in space (Schlesinger and Pilmanis 1998) and time (Austin et al. 2004). Shrubs in drylands exhibit a two-phase mosaic of patchy and clumped distribution (Aguiar and Sala 1999) due to the balance of competition for limited water and nutrients on one hand and moderation of the harsh environment on the other (McCluney et al. 2012). Islands of fertility can develop beneath shrub canopies where the availability of soil C and nitrogen (N) is coupled to inputs from plant litter and exudates. These inputs are very limited in the interspaces between shrubs (Garcia-Moya and McKell 1970). Therefore, both the magnitude of R s and its sensitivity to changes in temperature and soil water content are likely to differ between shrub islands and interspaces, such that microtopographic variation in R s in shrubby drylands may be regulated by plant inputs (Wang et al. 2015). The presence of substantial biological soil crust (biocrust; a photosynthetic soil cover of lichens, mosses, and/or cyanobacteria) and annual plant cover in interspaces may complicate this prediction (Castillo-Monroy et al. 2011), and also deserve inclusion in our consideration and prediction of dryland C cycling.

The temperature sensitivity of R s in drylands is a matter of some debate. In general, we know that temperature can increase R s directly via its effect on enzyme kinetics and diffusion rates (Davidson et al. 2014). At the same time, a number of empirical studies (e.g., Cable et al. 2011), as well as ecosystem models (e.g., Burke et al. 2003; Adair et al. 2008), indicate negative temperature sensitivity of R s above an optimal temperature, and multiple mechanisms have been proposed to explain this pattern. First, all organisms can be negatively affected by high temperatures above a certain threshold of thermotolerance (e.g., Lepock 2003), which varies substantially due to organismal adaptation to the environment. Bacterial growth has been shown to decline substantially above 40 °C in the Chihuahua desert (van Gestel et al. 2013), which might cause a decline in R s above that temperature. However, numerous other studies have indicated increasing R s across a very wide range of temperatures, even in much colder regions (e.g., Pietikäinen et al. 2005), and there is little a priori reason to think that organisms adapted to a hot desert environment would be directly inhibited by temperatures within the range they regularly experience, since organismal adaption to far higher temperatures (such as thermophilic bacteria) is not uncommon. Macromolecular rate theory similarly predicts declining reaction rates above an optimum temperature due to temperature-dependent activation energy, without suggesting direct thermal inhibition of organism function at moderately high temperatures (Shipper et al. 2014).

Alternatively, the co-occurrence of extremely hot and dry soil conditions may explain the apparent negative temperature sensitivity of R s observed at high temperatures in drylands. Generally, pulsed water availability regulates soil biogeochemical cycles in drylands (Noy-Meir 1973; Austin et al. 2004), such that soil communities and biogeochemical cycles are highly responsive to subtle shifts in precipitation (Nielsen and Ball 2015; Reed et al. 2012). Soil C cycling is closely linked to precipitation pulses (Huxman et al. 2004), as well as the antecedent soil moisture conditions (Barron-Gafford et al. 2014; Cable et al. 2013; Wertin et al. 2012). In soil, water availability influences the diffusion of nutrients and oxygen to respiring organisms (Davidson et al. 2012) and at low levels may directly limit respiration by soil organisms via effects on hydration and cellular function. Not only does soil moisture directly affect R s , but moisture also effects the temperature sensitivity of R s in ways that vary daily (Wang et al. 2014), seasonally (Tucker et al. 2016), and that differ among dryland regions (Cable et al. 2011). It is important to understand that these effects are generally interactive, not additive, such that understanding the climate sensitivity of R −s requires accounting for the interaction of temperature and moisture responses across the full range of conditions likely to be experienced.

A range of empirical and process-based models are currently implemented for understanding temperature and moisture responses of soil respiration (Sierra et al. 2015). Commonly used temperature response functions include simple exponential, Q10, Arrhenius, Lloyd and Taylor (Lloyd and Taylor 1994), and Century-type (Parton et al. 1994) functions, all of which make different predictions about the temperature sensitivity of R s . When temperature sensitivity is calculated as the multiplicative increase of R s over a 10 °C increase in temperature (i.e., as the Q10), these predictions range from static temperature sensitivity (simple exponential, Q10), to temperature-dependent temperature sensitivity that is either asymptotic (Lloyd and Taylor) or becomes negative above an optimal temperature (Century). When temperature sensitivity is calculated as the derivative of the function with respect to temperature, all of the temperature functions show temperature-dependent temperature sensitivity. Our analysis primarily focuses on the first definition, since it is more commonly implemented in soil respiration studies. Similarly there exist numerous functions for modeling the response of R s to soil moisture, which indicate linear (Demeter Foley 1995), saturating (Gompertz, Janssens et al. 2001), or parabolic (Savage et al. 2009) responses to volumetric water content (θ) and log-linear responses to soil water potential (ψ) (Manzoni et al. 2014). In general, the approach to modeling temperature × moisture interactions is to multiply these functions (as is done in this study), and this general approach can be extended to more detailed process models (e.g., Davidson et al. 2012, 2014). Nevertheless, rigorous quantitative and empirical evaluation among these models of R s is lacking for most ecosystems and, due to the complexities described in the preceding paragraphs, the appropriate model for dryland moisture by temperature responses is a critical uncertainty that limits our ability to predict global C cycle responses to climate change (Ahlström et al. 2015; Sierra et al. 2015).

To address this knowledge gap, in this study we used a dryland litter manipulation experiment to evaluate the temperature and moisture sensitivity of R s , beneath shrubs and in shrub interspaces, under varying levels of litter addition in a cold desert ecosystem on the Colorado Plateau, USA. A Bayesian approach to data analysis allowed us to rigorously compare competing hypotheses of the temperature and moisture controls on R s , with the goal of improving a quantitative understanding of dryland C fluxes. Our primary hypothesis was that reduced R s at high temperatures indicates water limitation, not negative temperature sensitivity. Thus, after appropriately accounting for water limitation, a model with an exponential temperature response would predict R s better than a model that with negative temperature sensitivity above an optimum temperature. Further, we hypothesized that due to low productivity, dryland soil respiration is C limited, and the response to litter additions should be highest in the interspaces, which are likely to be even more C limited than soils beneath shrub canopies, and the addition of new, high quality litter should result in reduced temperature sensitivity of soil respiration based on the quality-Q10 relationship (Fierer et al. 2005). An alternative hypothesis was that either older soil organic matter (SOM) or rhizosphere respiration drives higher respiration beneath shrub canopies than interspaces, rather than differences in new litter C, leading to the prediction that the difference of R s between shrub canopies and interspaces would be greater than the response of R s across the range of litter additions in either group.

Materials and methods

Field and lab measurements

The data described here were collected as part of a larger cross-site experiment, which has the goals of: (1) determining how variation in litter inputs affects the soil biogeochemical cycling of dryland ecosystems, (2) assessing the fate of decomposing litter organic matter in drylands, (3) investigating biological and physical controls over soil organic matter storage, and (4) elucidating the factors that regulate spatial variability in soil C and nutrient pools in the context of woody vegetation (‘islands of fertility’). The experimental design was modified from the Detritus Input and Removal Treatments (DIRT) experiment described by Nadelhoffer et al. (2006), where litter input manipulations have been made at eight mesic, closed canopy forests to determine how plant processes influence humus formation over decadal time scales. The research described in this paper is a part of the Dryland Detritus Input and Removal Treatments (D-DIRT) network, and currently the other sites are at the Santa Rita Experimental Range in southern Arizona, USA (led by Heather Throop) and the Reynolds Creek Experimental Watershed in southwestern Idaho, USA (led by Marie-Anne de Graaff).

The site used in this experiment is near Castle Valley, UT (36.675N, −109.416W) and has an elevation of approximately 1310 m, a mean annual temperature (MAT) of 13 °C, and a mean annual precipitation of 269 mm. The soils are a shallow, calcareous sandy loam aridisol and the vegetation is a mix of grasses and shrubs. The dominant vascular plant at the site is Atriplex confertifolia (C4 perennial shrub), with Achnatherum hymenoides (C3 perennial grass) and Gutierrezia sarothrae (C4 perennial shrub) also common. The site has a well-developed late successional biological soil crust community dominated by Collema spp. lichens and the moss Syntrichia caninervis.

The experimental design at this site includes 7 litter manipulation treatments: three treatments in areas associated with Atriplex confertifolia and four treatments in areas between vascular plants (i.e., plant interspace). There are five replicate plots for each treatment and type, for a total of 35 plots. For all 15 plots associated with A. confertifolia, each plot was created as a polygon with the shrub at its center. We created a rectangle around each shrub using the shrub’s longest direction as the long end of the polygon, adding 10 cm to the length of the shrub at each end. We used the perpendicular direction from this long-axis and added 8 cm onto the shrub on each side to create a boundary that encompassed both the shrub and soil surfaces both beneath the shrub and outside of the shrub’s canopy. A rebar stake was placed at each corner of the plot and a 10 cm tall fiberglass mesh border was connected to the rebar corners to inhibit litter losses and additions to the plots following treatment application.

Plots in the plant interspace were placed a minimum of 0.5 m from any vascular plant and were 50 cm × 50 cm in size. A rebar stake was placed at each corner of the plot and an 8 cm tall fiberglass mesh border was connected to the rebar corners to inhibit litter losses and additions to the plots following treatment application. For shrub and plant interspace plots, litter was collected by hand: litter collected from beneath the shrubs was placed into one set of containers and litter collected from plant interspace was placed into another. Litter from both areas was weighed and gently mixed, and then litter was returned to the plots with three litter amendments. Five plots received no litter following collection (0×), five plots received the average of the litter mass collected from all plots (control; for shrub plots, litter mass returned was determined based on the plot’s area, which varied among plots due to variations in shrub size), and five plots received twice the average litter mass (2×; Table 1). In addition, the plant interspaces had one additional treatment (n = 5), where the amount of litter added was the control amount added to the shrub plots (which was a much higher amount of litter than any of the other interspace treatments; Table 1).

Table 1 Litter amendments (g litter C m−2)
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Soil respiration (R s ) was monitored in each plot as follows. A 2 cm tall permanent soil collar (10 cm in diameter) was placed into each plot, with 1 cm pushed into the soil and 1 cm protruding out of the soil. We chose not to insert collars deeper into the soil profile because we wanted to avoid severing roots, which has been shown to substantially decrease measured R s in proportion to the depth of collar insertion (Heinemeyer et al. 2011). The tradeoff is increased potential for CO2 back-diffusion into the soil as concentrations build up in the chamber, however, due to our short measurement interval and relatively small concentration changes during the measurement period, it is unlikely that this was a major issue. R s measurements were made between 11:00 am and 1:00 pm using a LiCor 8100 Soil Gas Flux System (LiCor Bioscience, Lincoln, Nebraska, USA), using a 10 s purge, followed by a 2 min measurement interval. R s measurements were made monthly from October, 2013 to November, 2014, except for months when snow covered the ground. We excluded the January 2013 measurements, because soil moisture data were not collected during this sampling event. We did not use a small portion of the collected data due to either poor fits based on the internal flux calculation provided by the Licor software, or due to negative estimates of Rs. A total of eight measurement dates over the year were used in this analysis. An opaque chamber was used in conjunction with the LiCor system, thus the R s values were dark measurements, however, C assimilation of the biocrust community may not have been fully eliminated. Based on our evaluation of the patterns of reference respiration [R ref (which is defined in Eq. 2 below)] across the different levels of litter addition (ranging from 0 to 100 % ground cover)—including respiration from litter treatments that would have dramatically reduced light and thus photosynthesis—we feel confident the R s responses documented here are not artifacts of C assimilation by biocrust. Nevertheless, some uncertainty in our parameter estimates is likely attributed to this methodological limitation.

Volumetric water content (θ) and soil temperature (T) at 5 cm depth were collected concurrently with each R s measurement using an ECH2O volumetric water content probe and a soil temperature thermistor (Licor Biosciences) connected to the 8100 Soil Gas Flux System. To convert field measurements of θ to water potential (ψ), soil water release curves were generated using a WP4C Dewpoint Potentiameter (Scanlon et al. 2002, Decagon Devices, Pullman, WA) across a range of θ for soils from a subset of plots spanning the site in August 2015. Samples were then oven dried at 105 °C for 48 h to determine θ, which was fit to the measured ψ using non-linear regression in the ‘R’ statistical environment. For each measure of θ in the field, water potential (ψ) was then calculated from θ based on these water release curves.

Modeling and data analysis

The models

R s data were analyzed in the context of 20 (four temperature response functions × 5 water response functions) competing models of temperature and moisture controls on soil respiration to better understand the functional response of the soil C flux to variable climate conditions. Each of the i = 302 observation of R s were assumed to be normally distributed around a latent “true” respiration value µR i with error σ R .

$$R_{s,i} \sim Normal\,(\mu R_{i} ,\sigma_{R} )$$
(1)

The latent respiration µR was modeled as a multiplicative function of a reference rate (R ref ), soil water content function (f(W = θ or ψ)), temperature response function (f(T)), and a block random effect (ε block ), accounting for inter-block differences not explained by modeled covariates.

$$\mu R_{i} = Rref_{treatment} \times f(W_{i} ) \times f(T_{i} ) + \varepsilon_{block}$$
(2)

The reference respiration rate (which is the value of µR at optimum θ (M opt ) and the reference temperature (20 °C = 293.15 K) was assumed to take on values somewhere between 0 and 10 µmol m2 s−1, with a mean that varied by treatment (i.e., 7 levels encompassing each combination of shrub vs. interspace and litter addition).

$$\text{R} ref_{treatment} \sim uniform\,(0,10)$$
(3)

We implemented multiple temperature response functions (4i, 4ii, 4iii), capturing a range of hypotheses about the temperature sensitivity of soil respiration including a simple exponential function (4i) with constant temperature sensitivity across all temperatures, a Lloyd and Taylor function (4ii) (Lloyd and Taylor 1994) in which temperature sensitivity declines with increasing temperature but is always positive, and a Century-type function (4iii) (Parton et al. 1994) in which temperature sensitivity is negative above an optimum temperature. In the following equations the subscript, ‘treatment’ refers to parameters that were estimated separately for each of the seven treatment levels (Table 1), and i = 302 individual observations.

$$f(T_{i} ) = \exp \,(\beta_{treatment} \times T_{i} )$$
(4i)
$$f(T_{i} ) = \,\exp \,\left( {E_{o} \times \left( {\frac{1}{{Tref - To_{treatment} }} - \frac{1}{{T_{i} - To_{treatment} }}} \right)} \right)$$
(4ii)
$$f(T_{i} ) = \exp \,\left( {\frac{0.2}{2.63} \times \left( {1 - \left( {\frac{{T_{\hbox{max} } - T_{i} }}{{Topt_{treatment} - T_{i} }}} \right)^{2.63} } \right) \times \left( {\frac{{T_{\hbox{max} } - T_{i} }}{{Topt_{treatment} - T_{i} }}} \right)^{0.2} } \right)$$
(4iii)

Similarly, four functions for the response of R s to soil water content were implemented (5i, 5ii, 5iii and 5iv), including three functions of volumetric water content (θ): (5i) a linear function (Demeter) (Foley 1995), (5ii) a saturating function (Gompertz) (Janssens et al. 2001), (5iii) a parabolic function (Savage et al. 2009), and (5iv) a function of soil water potential (ψ) (Moyano et al. 2013) capturing a range of hypotheses about the moisture sensitivity of soil respiration. Different parameter values were not estimated for the litter*vegetation levels because our primary interest in this case was to evaluate the different moisture functions, not the treatment effect on soil moisture responses.

$$f(\theta ) = \alpha + (1 - \alpha ) \times \frac{{\theta_{i} }}{{\theta_{sat} }}$$
(5i)
$$f(\theta_{i} ) = \exp \,\left( { - \exp \left( {\alpha - \beta \times \frac{{\theta_{i} }}{{\theta_{sat} }}} \right)} \right)$$
(5ii)
$$f(\theta_{i} ) = D\left( {\frac{{\theta_{i} }}{{\theta_{sat} }} - \theta_{opt} } \right)^{2}$$
(5iii)
$$f(\psi_{i} ) = 1 - \left( {\frac{{\log_{10} \psi_{i} - \log_{10} \psi opt}}{{\log_{10} \psi_{\hbox{min} } - \log_{10} \psi_{opt} }}} \right)^{\alpha }$$
(5iv)

In addition, the null models of temperature and moisture (i.e., f(T i ) = 1, f(θ) = 1, such that R s is not a function of T or θ, respectively) were implemented to test the corresponding null hypotheses. The factorial combination of these temperature (4i, 4ii, 4iii) and moisture (5i, 5ii, 5iii and 5iv) functions were run, along with the null models, for a total of 20 competing models. Finally, a block random effect was incorporated as \(\varepsilon_{block} \sim Normal(0,\sigma_{\varepsilon } )\) to deal with potential inter-block differences, with the appropriate sum-to-zero constraint.

Statistical implementation

This data-model was implemented in the Stan Bayesian statistical software package (Stan Development Team. 2015. Stan Modeling Language Users Guide and Reference Manual, Version 2.7.0.) within the R (3.2.1) statistical computing environment using Hamiltonian Monte Carlo for sampling from the posterior distribution. We ran 12,500 iterations each of three Markov chains after the warmup period of 12,500 iterations to ensure adequate posterior sample size; the warmup period was sufficient to ensure convergence, which was evaluated using the potential scale reduction factor on split chains (\(\hat{R}\), where \(\hat{R} = 1\) at convergence). Model comparison was done using the Watanabe-Akaike Widely Applicable Information Criterion (Vehtari and Gelman 2014). Details of the modeling approach, including code and data, are provided in Supplementary material 1. Prior probability distributions and posterior mean and 95 % credible intervals for each parameter for each model are provided as Supplementary material 2.

Results

Soil volumetric water content (θ) and temperature (T) varied significantly over the course of the year (Fig. 1a, p < 0.001 for both) and were weakly negatively correlated (Fig. 1b), with maximum T coinciding with minimum θ. θ did not vary significantly by vegetation (p = 0.285) or litter treatment (p = 0.490); T was consistently warmer (average = +1.69 °C) in interspace plots than near shrubs (p < 0.001), but did not vary by litter treatment (p = 0.261). Mean observed soil CO2 efflux (R s ) (open circles–solid lines, Fig. 2) peaked in August 2014, coincident with peaks of both T and θ. R s increased with increasing θ, and increased from 5 to 30 °C temperature at 5 cm depth, thereafter declining sharply to the maximum observed temperature of 46.5 °C.

Fig. 1
figure 1

a Mean soil water (θ) and temperature (T) by treatment for each date, cover type, and litter treatment. Soil temperature values are shown with solid lines and closed circles and soil water content is shown with dotted lines and open circles. Values collected from the plots under shrubs are shown in red and those from plant interspaces are in black. Because there were no significant differences across litter treatments, these are shown as individual lines but not distinguished in the figure. b Volumetric water content (θ) versus temperature (T) at 5 cm depth in the soil. (Color figure online)

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Fig. 2
figure 2

Observed (solid lines—closed circles) and predicted (dashed lines—open circles) R s for shrub (red) and interspace (black) locations. Values are the mean across replicates by litter treatment and sampling date

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Our data-model integration approach conclusively supports the inclusion of interacting temperature and moisture functions for predicting R s (Fig. 3), based on high WAIC values (indicating poor model fit) for all models excluding either temperature or water functions. The Gompertz function for soil moisture (sharp increase in R s with small increases in θ at low θ) was the best fit in our system. The temperature functions were approximately equally good, although the parameter values for the Century model (modeled Topt = 44.12 [41.07, 46.33] and Tmax = 59.11 [55.91, 60.83], compared to default values of T−opt = 35 and Tmax = 45) effectively simplify this function to a near-exponential increase over the range of temperatures observed in the study. Because previous research indicates that the Lloyd and Taylor model captures temperature responses better than the simple exponential model (Lloyd and Taylor 1994), we focus the following analysis on the Lloyd and Taylor model results.

Fig. 3
figure 3

Watanabe-Akaike Information Criterion for model fit, for each of 16 combinations of water and temperature functions for R s . Columns correspond to different temperature functions (f(T)) and rows correspond to the different water functions (f(W = θ or ψ)). The line plots above and to the right of the matrix display the marginal (i.e., without considering T × W interactions) shape of the curve produced by each function using standard parameter values. The smaller values (dark green; <600) indicate better models, the larger values (red; >880) indicate worse models. Excluding either temperature or water from the models results in unviable fits to R s data. With any of the temperature functions, the best support was for the Gompertz function; however, it should be noted that the parameter values estimated via Hamiltonian Monte Carlo for each temperature function result in a curve that is most simply approximated with a simple exponential function. (Color figure online)

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The combined Lloyd and Taylor—Gompertz model fit the data well, explaining 76 % of the variation in measured values (Fig. 4a), the residuals were evenly distributed around 0 across the range of predictions (Fig. 4a inset). The modeled temporal patterns are indistinguishable from observed patterns (Fig. 3 dashed lines). During periods of peak respiration, shrub plots showed substantially higher R s than interspaces, while values converged during periods of low R s . Observed values of R s generally increased from θ < 0.02 to θ ≈ 0.07 m3 m−3, and model predicted values showed the same pattern (Fig. 4b). The observed peak of R s at approximately 30 °C, and subsequent sharp decline (Fig. 4c), were well-captured by our model, which is somewhat surprising given the use of an exponential temperature response function, and reflects the dry soil conditions at high temperatures.

Fig. 4
figure 4

a Left panel Observed (x axis) versus predicted (y axis) R s based on the Lloyd and Taylor—Gompertz model. Solid line indicates the one-to-one line, and residuals of the predictions compared to the one-to-one line are presented in the inset plot, with observed values on the x axis of the inset. Error bars indicate 95 % credible intervals. b Middle panel Observed and predicted R s versus soil temperature (T) and c Right panel: soil volumetric water content (θ). The y axis has the same units in all three plots, although in plot a it refers only to predicted R s , while in b and c it refers to both observed and predicted values

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Parameters E o and T o in the Lloyd and Taylor temperature function (Eq. 4ii.) did not differ significantly among litter treatments or between shrub and interspaces—the mean and 95 % credible interval across treatments were −E o  = 318 [222.77, 427.53] and T o  = 220.12 [200.1, 236.99]—and indicated an exponential increase of R s with T across the full observed temperature range (Fig. 5a). Q10 temperature sensitivity (5i) calculated as a function of temperature (Cable et al. 2011; Tucker et al. 2013, 2016) decreased from ~3.4 to ~1.2 between 5 and 46.5 °C, while temperature sensitivity calculated as df(T)/dT (calculated as the numeric derivative as described by Sierra et al. 2015) increased from 0.075 to 0.22 µmol CO2 m−2 s−1 °C−1 across the same range. The Gompertz moisture sensitivity function indicated increasing R s with increasing θ between 0 and ~0.07 m3 H−2O m−3 soil, and little increase above that level (Fig. 5b). Moisture sensitivity (calculated as the numeric derivative df(θ)/dθ as described by Sierra et al. 2015) was highest at θ = ~0.04, decreasing above and below that value (Fig. 5b). Water holding capacity in these soils is θ = ~0.22, such that peak moisture sensitivity was at 18 % of WHC, and f(θ) saturated at ~32 % of WHC.

Fig. 5
figure 5

a f(T) (filled circles with error bars, left y axis), Q10 (dotted line, first right y axis) and df(T)/dT (dashed line, second right y axis) versus temperature (T), where f(T) is the temperature response of R s from Eq. 4ii. b f(θ) (filled circles with error bars) and df(θ)/dθ (dashed line) versus θ. Error bars indicate 95 % credible intervals, where f(θ) is the volumetric water content from Eq. 5ii. In a, the temperature response of R s  − f(T)—increases with T, and the change f(T) with a change in T − df(T)/dt—is positive, indicating positive temperature sensitivity across the full range of observed temperatures. Q10 decreases with increasing temperature, but is always greater than 1, indicating declining but nonetheless positive temperature sensitivity. In b the volumetric water content response of R s −f(θ)—increases sharply between θ = 0.02 and 0.07, indicating high moisture sensitivity under very dry conditions. The peak moisture sensitivity—df(θ)/dθ—occurs near θ = 0.04

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Reference respiration (R ref , Fig. 6) was higher beneath shrubs than in the interspace plots, regardless of litter amendment (including the amendment where the relatively high amounts of shrub litter were added to interspace plots), suggesting that either decomposition of older SOM or root and rhizosphere respiration (rather than new litter respiration) accounts for the difference. There were no significant differences among litter amendment levels beneath the shrubs. In contrast, in the interspaces, R ref increased from control to double litter to ‘shrub’ litter, although the no litter value did not follow this pattern, and was equal to the shrub litter value, undermining the most obvious mechanistic interpretation.

Fig. 6
figure 6

R ref for each cover type and litter treatment level. R ref is the modeled respiration rate at 20 °C and optimal θ. Grey bars are interspace plots and white bars are shrub plots. Error bars indicate 95 % credible intervals. Significant differences occur where credible intervals of one treatment × cover type do not overlap the mean of another, these significant differences are indicated by lowercase letters within each bar

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Discussion

The results presented here demonstrate that apparent negative temperature sensitivity of R s at high temperatures in our study system is driven primarily by water limitation under co-occurring hot-dry conditions—sensitivity to volumetric water content (θ) was very high below ~0.06 cm3 cm−3 but was low above that level. Temperature sensitivity of R s was positive across the entire range of observed temperatures after accounting for the effects of soil water content, although sensitivity decreased with increasing temperature. While temperature sensitivity (Q10) and the reference respiration rate (R ref ) showed no consistent pattern of variation among litter amendment levels, R ref was ~35 % higher under shrubs than in interspaces, suggesting that respiration from the rhizosphere and potentially older SOM are much more important drivers of R s in this system than respiration of new litter inputs. Taken together, our modeling approach allowed us to disentangle the effects of soil moisture, temperature, and litter inputs on R s to demonstrate that the choice of water functions is the most critical attribute for best fitting the observed R s . A dominant role of soil moisture in regulating dryland soil CO2 efflux is not surprising, but the multi-model approach used here elucidates the water functions that are the most powerful, as well as the key interactions between soil moisture and temperature and an unpredictably subtle effect of large changes to litter inputs.

Emerging data suggest that drylands play a particularly important role in driving interannual patterns and overall trends in atmospheric CO2 concentrations and land C stocks (Poulter et al. 2014; Ahlström et al. 2015). Our multi-model comparison framework provides useful information for modeling the soil C cycle in drylands, in particular showing that R s in drylands cannot be approximated even roughly without the inclusion of both temperature and moisture response functions. The best-fit moisture function (5ii; Gompertz) predicts high moisture sensitivity of R s at very low volumetric water content (θ) but no moisture sensitivity at high θ (>0.08 m3 m−3 in this study). This result makes intuitive sense in the context of desert climates and the corresponding adaptations of desert organisms to occasional water pulses and long dry periods (Austin et al. 2004) and highlights threshold values of R s response that could be useful and testable in other drylands. In wetter systems it is likely that either the parabolic (5iii) or water potential (5iv) functions, which reduce R s as water saturation produces anoxic conditions, would be superior, highlighting the potential importance of biome- or climate-specific relationships between soil moisture, temperature, and R s . Indeed, we expected that the water potential (ψ) function (5iv; Moyano et al. 2013) would improve model performance but, contrary to our expectations, the Gompertz (5ii) model out-performed the water potential model. This result may indicate that substrate and nutrient diffusion are more important factors in determining the moisture response of R s than is the balance of osmotic potential and soil water potential of microbes and roots in soil (Manzoni et al. 2014). It is worth noting that the water potential function (5iv) was developed over a very large range of water potential values, including very wet locations, while water potential values at our site are restricted to the drier end of this spectrum. Given this caveat, further development on the appropriate function to best capture the role of water potential is merited, because the water potential function was tied for the 2nd best function.

The exact temperature response function used was surprisingly not very important: the model fit as evaluated via WAIC was similar among the simple exponential (4i), Lloyd and Taylor (4ii) and Century (4iii) functions. However, we must emphasize that responses produced via our parameter estimation approach converged across these three functions: f(T) increased with temperature across the full range of T observed in the study. To clarify, the Century function (4iii) can allow for negative temperature sensitivity above an optimum temperature, but the best-fit parameters for the Century model in our study indicated an optimum temperature near the maximum observed during the experiment (46.5 °C), such that it was effectively also an exponential temperature response function. In contrast, the standard literature-derived parameter values for these functions produce very different functional response of R s to temperature, and our study indicates that these values should not be used without careful evaluation. At the minimum, ecosystem-specific calibration is required for rigorous implementation of these temperature response functions. The best fit model does suggest decreasing Q10 temperature sensitivity and a shallowing of df(T)/dT temperature sensitivity with increasing temperature (Fig. 5a). At some temperature above those observed in this study we should expect respiration to show negative temperature sensitivity, but it is not clear what that temperature threshold is, or whether it is relevant in the context of predicted climate change.

We provide direct evidence to address to the question posed by Sierra et al. (2015) regarding whether R s rates decline at higher temperatures because of moisture limitation rather than negative temperature effects—our results suggest that over the very wide temperature range in our study (5–46.5 °C) R s is a positive function of soil temperature, and the sharp decline at high temperatures is driven by soil drying. Since we do not partition autotrophic and heterotrophic respiration, we cannot conclusively say that decomposition rates do not decline at higher temperatures, but any declines in heterotrophic respiration would have to be matched by increases in other CO2 sources to explain our results. For instance, laboratory incubations indicate that bacterial growth in hot desert (Chihuahua) soils increases up to 40 °C and declines above that temperature (van Gestel et al. 2013); however, in that study bacterial growth at ~50 °C was nonetheless greater than at ~25 °C. Thus, one explanation for the consistently positive temperature sensitivity of R s is that growth and maintenance respiration become increasingly decoupled above a growth optimum (Pietikäinen et al. 2005), such that the net temperature sensitivity of heterotrophic respiration is still positive

Decomposition and autotrophic respiration as drivers of surface CO2 efflux

Over the course of the measurements, reference respiration (R ref ) beneath shrubs was 46 % higher than in the biocrust-dominated interspaces, which is well-aligned with the few existing similar data from other drylands. For example, over 4 years of monthly, midday measurements in a semiarid ecosystem in Spain, Castillo-Monroy et al. (2011) observed values of R o (analogous to R ref ) beneath shrub canopies that were 22 and ~75 % greater than in surrounding bare soil and biocrust-dominated interspaces, respectively. For both our and the Castillo-Monroy et al. (2011) R s data, these patterns could be interpreted as the result of heterotrophic respiration due to higher SOM and litter inputs beneath the shrubs, and/or as higher autotrophic (i.e., root and rhizosphere) respiration beneath the shrubs. Because in our study the litter removal/addition had no clear effect on reference respiration, we suggest that autotrophic respiration beneath shrubs was more important than new aboveground litter as a source of R s . This supports our hypothesis that root and rhizosphere respiration drives the higher respiration beneath shrub canopies than interspaces, rather than difference in C availability for decomposition. Thus, soil respiration in this system is likely closely tied to recent aboveground biotic activity, especially photosynthesis, of shrubs and subsequent transfer of photosynthate belowground. The role of older SOM in driving heterotrophic patterns of CO2 efflux warrants more attention and will be addressed as the litter manipulation treatments age.

The lack of stimulation of R ref or change in T o in response to litter addition in the interspaces is intriguing. The ‘shrub’ litter addition in the plant interspace plots represents a large increase in the C density of the interspaces (a ~650 % increase in litter C and a ~45 % increase in total C of the upper 5 cm; Table 1). The added litter also increased the total surface area for colonization by decomposers, and should increase the decomposability (i.e., quality) of the soil C because fresh litter is generally more labile than older SOM. Thus, a strong prediction was merited that R ref would increase with litter addition. As formulated in Eq. 2, R ref implicitly incorporates effects driven by quantities of either substrate (i.e., litter, SOM) or biomass of roots and microbes (see Tucker et al. (2013) for a model which this dependence is modeled explicitly). Other ecosystems have shown a strong and rapid response to altered litter inputs; for example, a doubling of litter mass (2x) in a Costa Rica tropical rain forest showed 43 % more CO2 efflux relative to plots where all litter was removed (0×; measurements made weekly over the course of 2 years; Leff et al. 2012). It merits consideration that in drylands, photodegradation causes substantial decomposition of surface litter (Barnes et al. 2015), and this process would not have been captured by our measurement and modeling approaches. A somewhat weaker prediction was that T o would decrease (i.e., temperature sensitivity would decrease) with litter addition because in many studies temperature sensitivity is inversely related to substrate quality (Fierer et al. 2005; Leifeld and Fuhrer 2005). It is possible that in this system the effects of altered litter inputs take much longer to emerge, but over the timeline of this research neither of the predictions were supported by our model. Thus R s in this system is more limited by environmental constraints imposed by water limitation than C limitation.

The importance of drylands in regulating the global C cycle is debated, with some contemporary data suggesting a stronger role for drylands than has previously been considered. Indeed, recent modeling and remote sensing work indicates that semi-arid systems dominate the trajectory of the global C sink, as well as inter-annual variability in net biome production, (Ahlström et al. 2015; Poulter et al. 2014). Our results demonstrate high temperature and moisture sensitivity of soil C cycling in a cold desert system, with a likely strong linkage to intra-annual plant productivity, which would provide mechanistic support for these global patterns. The question remains, however, whether the amount of C entering and leaving drylands on both a per unit area and a global basis is large enough to be quantitatively important compared to the large pools and fluxes occurring in tropical forests and permafrost-region soils (Schlesinger et al. 2009). To put our results into context, we extracted maximum R s values reported for 99 studies from the Global Soil Respiration Database (Bond-Lamberty and Thomson 2010), and compared them to mean annual precipitation (MAP) and mean annual temperature (MAT) (Supplement 3). Generally, maximum R s increased with MAT and MAP interactively. This pattern likely occurs primarily as a response to the high C inputs resulting from elevated net primary productivity in areas with high MAT and MAP (Davidson and Janssens 2006), and secondarily as a direct response of decomposition and root respiration to these climate drivers. Importantly, at our warm and dry study site the maximum R s was 25 % higher than the global average reported across all sites, as well as higher than predictions based on the multiple linear regression of maximum R s against MAT × MAP across all studies. This pattern demonstrates that this cold desert ecosystem has the capacity for significant rates of C cycling, notwithstanding the low pool sizes and strong environmental limitations on fluxes. Coupling this to observations of highly variable net primary production (Poulter et al. 2014) in dryland systems suggests a dryland C cycle that may continue to be dynamically responsive to future climate changes.

Caveats and uncertainties

We measured soil surface efflux of CO2, which is a composite flux with components that may respond differently to environmental drivers (Ryan and Law 2005). One potential source of uncertainty is C assimilation by soil crust organisms such as mosses, lichens, and cyanobacteria (e.g., Darrouzet-Nardi et al. 2015). Our respiration measurements were conducted in the dark, yet CO2 fixation might continue for some time in the dark. However, we do not believe this issue significantly affected our results based on the following logic: in the interspaces, litter removal and addition created a surface litter layer ranging from 0 to ~100 % cover, which should have had a measurable effect on soil C fixation rates via large effects on light reaching autotrophic biocrusts. This effect would have appeared most clearly as a reduction of R ref in the low litter treatments (via a photosynthetic draw down of CO2) relative to the high litter treatments, which we did not observe. Additionally, it is important to note that we do not partition heterotrophic and autotrophic respiration in this study, although it may be reasonable to assume that the two fluxes are responding similarly although most certainly not equally (e.g., Boone et al. 1998) to the temperature and moisture regime. Most ecosystem and earth system models consider the decomposition flux and root respiration separately, thus while our results probably extend to both fluxes, our parameters estimates cannot be used directly in these models. Additionally, significant autotrophic respiration potentially obscured the importance of litter addition as a factor in the decomposition flux. Finally, because we did not manipulate soil moisture and temperature in this study, we are lacking direct observation of the very hot-wet conditions predicted to have highest R s by our model.

Relevance to predicted climate change

High temperature coinciding with low soil moisture is a common feature of many deserts, and very low soil CO2 effluxes occur during hot-dry conditions, which has alternately been interpreted as negative temperature sensitivity or water limitation of soil respiration. Our study demonstrates R s increases with temperature and moisture across the ranges of both observed at our study site. Thus potentially large soil CO2 effluxes during brief hot and wet periods (i.e., pulses) may cause significant soil C loss, even accounting for the rarity of coinciding hot and wet conditions in desert soils. Similarly, no-analog future climates wherein historic relationships between soil temperature and moisture are decoupled may bring the more frequent occurrence of hot—wet conditions, thus necessitating an improved process based understanding of ecological responses to climate drivers (Williams and Jackson 2007). Climate models generally predict hotter conditions across our study region (although the range of precipitation forecasts is variable (Garfin et al. 2014), which without changes to precipitation would lead to declining surface water availability overall, but potentially greater variability (Seager et al. 2013). Combined with our results and recent observations of the importance of drylands in the terrestrial C cycle, the above possibilities suggest the moisture and temperature responses of R s in drylands such as our study system may be globally important regulators of fluxes of CO2 from the biosphere to the atmosphere.