A stochastic model for daily subsurface CO 2 concentration and related soil respiration Edoardo Daly a,b,c, * , A. Christopher Oishi b , Amilcare Porporato a,b , Gabriel G. Katul b,a a Department of Civil and Environmental Engineering, Duke University, Durham, NC, USA b Nicholas School of the Environment and Earth Sciences, Duke University, Durham, NC, USA c Department of Civil Engineering, Monash University, Building 60, Clayton Campus, Clayton, VIC 3800, Australia article info Article history: Received 4 December 2007 Received in revised form 25 March 2008 Accepted 2 April 2008 Available online 8 April 2008 Keywords: Soil CO 2 CO 2 pulses Soil respiration Rainfall abstract Near-surface soil CO 2 gas-phase concentration (C) and concomitant incident rainfall (P i ) and through-fall (P t ) depths were collected at different locations in a temperate pine forest every 30 min during the 2005 and 2006 growing seasons (and then averaged to the daily timescale). At the daily scale, C temporal vari- ations were well described by a sequence of monotonically decreasing functions interrupted by large positive jumps induced by rainfall events. A stochastic model was developed to link rainfall statistics responsible for these jumps to near-surface C dynamics. The model accounted for the effect of daily rain- fall variability, both in terms of timing and amount of water, and permitted an analytical derivation of the C probability density function (pdf) using the parameters of the rainfall pdf. Given the observed positive correlation between daily C and soil CO 2 fluxes to the atmosphere (F s ), the effects of various rainfall regimes on the statistics of F s can be deduced from the behavior of C under different climatic conditions. The predictions from this analytical model are consistent with flux measurements reported in manipu- lative experiments that varied rainfall amount and frequency. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction Soil CO 2 fluxes (F s ) to the atmosphere are the result of complex physical and biological processes that depend on soil properties, vegetation and microbial characteristics, and climatic conditions [12,29]. In particular, the effects of environmental fluctuations on F s , such as the rapid fluctuations in soil moisture and tempera- ture or the slow increase in atmospheric CO 2 concentration and nitrogen deposition, remain the subject of active research [10,13,21,22,32,46]. Soil respiration pulses following rainfall events have been ob- served in several ecosystems [15,36,44,47]. The importance of these pulses on annual respiration appears to vary across ecosys- tems. Lee et al. [42] found that post-rainfall increases in F s might represent approximately 16–21% of the annual soil carbon flux in a cool temperate deciduous forest in Japan, while the estimates of Lee et al. [43] in a mixed forest in Connecticut (USA) were be- tween 5% and 10%. Xu et al. [62] suggested that soil carbon losses by rainfall pulses might be comparable to annual net ecosystem carbon dioxide exchange in many terrestrial ecosystems, especially for arid and semiarid ones. A manipulative experiment in a grass- land ecosystem, described in Knapp et al. [40] and Harper et al. [30], concluded that F s is not only dependent on precipitation amounts but also on the frequency of rainfall occurrence. These findings open new questions on how changes in rainfall patterns modify soil respiratory components. This study is guided by the strong relationship between CO 2 fluxes and subsurface CO 2 concentrations, C, which now can be monitored at unprecedented time resolution using solid-state infrared gas analyzers [60]. When taken together, how the dynam- ics of C is impacted by pulsed rainfall, and the consequences of this rainfall intermittency on the dynamics of CO 2 fluxes from the soil to the atmosphere can now be explored. Numerous and complex interconnections between the physical and biological processes occur in the soil during and after rainfall events. During precipitation, water infiltration displaces an equiv- alent volume of air thereby enhancing air-phase CO 2 fluxes [29]. However, rainfall also reduces CO 2 fluxes because of the reduction in gas-phase soil CO 2 diffusivity (D). In fact, the increase in soil water content following rainfall events significantly reduces D thus favoring the build-up of higher CO 2 concentration levels [15,29,36] even if the CO 2 production remains unaltered. In addition to these physical effects, increased soil moisture levels can enhance micro- bial activity [5,35,45] by two mechanisms. The first is through the mineralization of non-biomass soil organic carbon, which becomes readily accessible to microbial attack following soil aggregate 0309-1708/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.advwatres.2008.04.001 * Corresponding author. Address: Department of Civil Engineering, Monash University, Building 60, Clayton Campus, Clayton, VIC 3800, Australia. Tel.: +61 3 9905 4979; fax: +61 3 9905 4944. E-mail addresses: Edoardo.Daly@eng.monash.edu.au (E. Daly), acoishi@duke.edu (A.C. Oishi), amilcare@duke.edu (A. Porporato), gaby@duke.edu (G.G. Katul). Advances in Water Resources 31 (2008) 987–994 Contents lists available at ScienceDirect Advances in Water Resources journal homepage: www.elsevier.com/locate/advwatres