Minirhizotron data were collected at the Nevada Desert FACE Facility (NDFF) located on the US Department of Energy's Nevada National Security Site (formerly Nevada Test Site) north of Las Vegas in the Mojave Desert. The Mojave Desert is one of the driest regions in North America with an average of 140 mm of precipitation each year. Rainfall each year is highly variable; during the 10 yr experiment (1997–2007), maximum and minimum hydrological year (October to September) precipitation totals were 328 mm (1997–1998) and 47 mm (2001–2002), respectively. Precipitation during the study is shown in Fig. 1. Vegetation of the site is characteristic of the Mojave Desert and dominated by the evergreen shrub Larrea tridentata (Sessé & Moc. ex DC) Coville (creosote bush) and the drought-deciduous shrub Ambrosia dumosa (A. Gray) Payne (bur-sage). Vegetation is sparse with < 20% of surface area covered by shrubs and perennial plants (Jordan et al., 1999).
The NDFF data used in this study consists of six plots, each a ring of 23 m diameter. Plots were assigned to one of two treatments: blowers that elevated atmospheric CO2 to 550 ppm (elevated CO2), and blower controls (ambient CO2). Each treatment was applied to three replicate plots. The CO2 treatments were applied 24 h per day each day of the year, except during periods of low temperature (to avoid adverse effects of air movement on plant energy balance) and high wind (to reduce CO2 consumption). During the period of minirhizotron observations (2003–2007), elevated CO2 averaged 511 ppm and ambient CO2 averaged 375 ppm. The CO2 application protocol necessitated an on-site automated weather station that recorded air temperature, wind speed, wind direction, humidity, and precipitation amounts.
A total of 28 minirhizotron tubes were installed in each plot and were distributed among three cover types (L. tridentata, A. dumosa, and community). Two minirhizotron tubes where placed under four individuals (i.e. ‘replicates’) of each of the two shrub species for a total of 16 tubes per plot, providing fine-root data on the two dominant species. The remaining 12 tubes were arranged into three transects (i.e. ‘replicates’) that were systematically located along radii from the plot center (Philips et al., 2006), providing data on the entire plant community.
Digital images (40 kb resolution) captured via a Bartz Technology field computer (Bartz Technology Corp., Santa Barbara, CA, USA) were analyzed by manually tracing individual roots using ROOTRACKER (David Tremmel, Duke University, Durham, NC, USA); production and loss are expressed as root length per image area (mm-1 d-1) (Ferguson & Nowak, 2011). Typical of minirhizotron studies, the timing of fine-root production (i.e. appearance of a new root) can be directly observed but timing of mortality cannot. Instead, actual mortality (i.e. loss of metabolic functions) occurred at some unknown time before observed root loss (i.e. when the root has decayed sufficiently to be classified as dead). We use 'loss' instead of 'mortality' here to emphasize this distinction.
Observations of root production, loss and standing crop were made approximately every 4 wk from January 28, 2003 until May 22, 2007 (52 sampling dates). Each tube was divided into 23 non-overlapping 11.5 mm × 9.1 mm frames (Ferguson & Nowak, 2011), and then grouped and averaged into four depth categories (0–25, 25–50, 50–75, and 75–100 cm after adjusting for the tube angle). The grouping was used because some frames were unobservable because of scratched tubes or rock obstructions and because grouping mitigated the large number of zeros and reduced the data set to a computationally tractable size. When converting continuous data to categorical, four categories are often used because four categories maintain a high degree of flexibility (i.e. a cubic effect of depth could still be estimated) but still keep the number of categories manageably small. Finally, we divided observed average production or loss by tube standing crop so that data are rates of production and loss per unit of standing crop. An example of observed temporal dynamics in standing crop of L. tridentata is given in Fig. 1.
Replicate tube observations were subsequently averaged to obtain a single value per each plot, cover type, depth and sampling date combination for several reasons. First, covariate information such as soil moisture was available only at the plot level. Second, extremely long Markov Chain Monte Carlo (MCMC) simulation times were exacerbated by microsite variability when data were not aggregated across tubes within each plot. Third, aggregation reduced the percentage of zero observations, which improved model behavior. Finally, because the experiment is intended to evaluate treatment effects at the landscape level and because treatment replicates are at the plot level, bypassing the computational difficulties of using the full dataset is justified.
To quantify the role of biological inertia, we categorized production rates into four states based on observed quantiles within each cover type. The first state corresponds to prior production being zero, and the other three states correspond to previous production being low, medium or high, where these categories are defined by the observed 33.3% and 66.6% quantiles of all observed production rates for each cover type. The loss inertia term is defined similarly, and inclusion of previous rates in the model can mathematically be thought of as a discretized autoregressive model of order one.
Five phenological periods are defined by the months October–November, December–February, March–April, May–June, and July–September. Each phenological period within a hydrological year (October 1 to the following September 31) had at least two and at most five sampling dates per year. These phenological periods correspond to autumn, winter, spring, early summer, and late summer, respectively, and represent distinctive periods of plant growth and seasonal precipitation and temperature (Rundel & Gibson, 1996). Winter corresponds to early green-up of leaves and initiation of fine-root growth. Spring characteristically has maximal fine-root production and microbial decomposition of previously expired roots. Early summer is defined by recently produced fine roots but continued loss of older roots. During late summer, the soil water content is low and drought-deciduous shrubs and annuals are senescing and losing leaves, and fine-root production and loss also tend to be low. During the fall dormancy phase, fine-root production is negligible and loss is generally lower than late summer.
Measurements of integrated soil water over two depths increments (0–20 and 0–50 cm) were made approximately once a month with soil moisture probes (time-domain reflectometer (TDR) and neutron probes). Because minirhizotron and soil water observation dates were not always concordant, we modeled soil water content to estimate a daily time-series of soil water values. We fitted the observed soil water and precipitation data to the one-dimensional soil water budget (SWB) model of Kemp et al. (1997) that incorporates transpiration, evaporation and infiltration. Evaporation was modeled using daily solar radiation and air temperature. Transpiration was a function of vapor pressure deficit, leaf area index and soil water potential. Water infiltration from precipitation events followed a 'bucket model' where the top soil layer is filled to the water holding capacity and any residual moisture drains to the layer below. We augmented the SWB model to allow for transport between layers using the Darcy–Richards equation. For each date with observed soil water data, we used the observed data as the starting point for the model and ran the model forward in time to predict soil water values up to the next date when soil water measurements were made. This model fitted the observed soil water data well enough () to scale an interpolation between soil moisture observations, even with intervening precipitation events. We then estimated a daily time-series of soil water content over the 0–50 cm profile.
Data synthesis approach
Over the 4-yr study period, which included periods of both high and low precipitation (Fig. 1), a large percentage of observations were associated with zero production or loss. Data that were non-zero, which indicated some amount of recordable production or loss, were highly skewed. These data attributes required a flexible modeling approach and prompted our choice to use a hierarchical Bayesian approach, which provides a useful framework when traditional statistics do not provide an easy solution. We fitted the same model to each cover type and parameters are estimated separately for each cover type.
Figure 1. Top: cumulative hydrological year precipitation during the years of the study. The horizontal gray line represents mean total annual precipitation. Bottom: Larrea tridentata standing crop of fine roots over time. After a drought during 2001 and 2002, L. tridentata standing crop at the beginning of 2003 was low. During the subsequent spring, standing crop increased for both ambient (red circles) and elevated (blue circles) treatments, but the elevated CO2 treatment added comparatively more fine-root standing crop. The subsequent loss of roots in late 2004 was more extreme under ambient CO2. However, ambient standing crop converged to the elevated standing crop during the El Niño event of 2005, when standing crop peaked. During the subsequent dry spell, both treatments had similar loss rates. Ambrosia dumosa and the entire community had similar patterns as those for L. tridentata.
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The model structures for production and loss were identical, and for brevity, we only describe the production model. To address the large number of zeros and skewed values, we assumed zero-inflated lognormal models for observed production rates. To simplify notation, for observation j (j = 1,2,…,1224), let represent the observed average production rate for a given plot, cover type, depth and sampling date. The likelihood for is defined by the mixture distribution:
- (Eqn 1)
Next, is described by a hierarchical mixed effects model that includes depth (d = 1, 2, 3, or 4 for 0–25, 25–50, 50–75, and 75–100 cm), treatment (t = 1 or 2 for ambient or elevated), inertia (i = 1, 2, 3, or 4 for zero, low, medium, or high prior production), plot (r =1, 2, 3 per treatment), hydrological year (hy = 1, 2,…, 5 for 2002–2003 through 2006–2007), phenological period (s = 1, 2,…, 5 for October–November, December–February, etc.), sampling occasion (o = 1, 2,…, 5) within a hydrological year and phenological period, and antecedent soil water (A). Thus, the model for is:
- (Eqn 3)
Finally, noninformative Normal(0,σ=100) priors were assigned to all fixed effects (, , , , , , , ) in Eqns 2 and 3; the priors are substantially wider than the corresponding marginal posterior distributions. Random effects (, , ) were assigned normal priors with zero mean and variance components , , and . Because there were only a small number of levels associated with each factor (hydrological year, date within phenological period and hydrological year, and plot within treatment), standard deviations for each random effect were assigned folded Cauchy priors to avoid posterior distributions with unrealistically heavy right tails (Gelman, 2006). Wide uniform priors were assigned to standard deviations in production rate, loss rate, and standing crop likelihoods (e.g. σ and ). The model was implemented in the Bayesian software package JAGS (Plummer, 2003) and three parallel MCMC chains were run for 100 000 iterations, Convergence was evaluated according to Gelman & Rubin (1992) diagnostics.