Trace Gas Emission in Chambers: A Non-Steady-State Diffusion Model

Non-steady-state (NSS) chambers are widely used to measure trace gas emissions from the Earth’s surface to the atmosphere. Unfortunately, traditional interpretations of time-dependent chamber concentrations often systematically underestimate predeployment exchange rates because they do not accurately represent the fundamental physics of diffusive soil gas transport that follows chamber deployment. To address this issue, we formally derived a time-dependent diffusion model applicable to NSS chamber observations and evaluated its performance using simulated chamber headspace CO2 concentration data generated by an independent, three-dimensional, numerical diffusion model. Using nonlinear regression to estimate the model parameters, we compared the performance of the non-steady-state diffusive flux estimator (NDFE) to that of the linear, quadratic, and steady-state diffusion models that are widely cited in the literature, determined its sensitivity to violation of the primary assumptions on which it is based, and addressed some of the practicalities of its application. In sharp contrast to the other models, NDFE proved an accurate and robust estimator of trace gas emissions across a wide range of soil, chamber design, and deployment scenarios. N CHAMBERS (Livingston and Hutchinson, 1995; Hutchinson and Livingston, 2002) are widely used to measure rates of trace gas exchange between the Earth’s surface and the atmosphere. Indeed, no other method has contributed more to current understanding of the magnitude and spatiotemporal variability of trace gas exchange rates or their process-level controls. Data from such studies have promoted understanding of C and nutrient dynamics, facilitated development of land use management strategies, and helped establish the relative importance of various greenhouse gas sources and sinks. Despite these important contributions, theoretical and empirical evidence indicates that flux densities derived from NSS chambers systematically and often significantly underestimate the rate of emissions that prevailed before chamber deployment (Matthias et al., 1978;Hutchinson and Mosier, 1981; Jury et al., 1982; Samuelsson, 1990; Anthony et al., 1995; Wagner et al., 1997; Pedersen et al., 2001; Davidson et al., 2002; Pumpanen et al., 2003; Hibbard et al., 2004; Livingston et al., 2005). This bias results not from inherent limitations of chambers themselves, but from long-held misconceptions regarding the interpretation of chamber headspace concentration data and, in particular, from the use of flux estimation models that fail to accurately represent the fundamental physics of diffusive soil gas transport in the presence of a NSS chamber. In practice, the predeployment flux density is estimated by first fitting an assumed model of chamber headspace concentration with time to the observed data and then projecting the instantaneous rate of change at the moment of chamber deployment. The most widely used model by far is the linearmodel, which assumes that emissions into the chamber headspace are constant throughout the deployment period. In fact, however, the rate of transport of a diffusing trace gas into the chamber headspace necessarily declines throughout deployment because any increase in the headspace concentration results in an immediate decline in the subsurface vertical concentration gradient driving that transport (Matthias et al., 1978; Hutchinson and Mosier, 1981; Jury et al., 1982; Samuelsson and Pettersson, 1984; Rolston, 1986; Hutchinson et al., 2000). The error in applying a linear model to inherently nonlinear concentration data has long been assumed negligible if recommended guidelines regarding chamber design, deployment, and sampling are followed to foster the appearance of linearity in the observed concentration data (Livingston and Hutchinson, 1995; Davidson et al., 2002; Hibbard et al., 2004); however, the resultant error is not negligible and thus the use of linear models has ensured that predeployment emission rates have been systematically and often substantially underestimated in nearly all NSS chamber applications (Matthias et al., 1978; Jury et al., 1982; Anthony et al., 1995; Hutchinson et al., 2000; Livingston et al., 2005). In recognition of this issue, nonlinear models, such as the physically based model proposed by Hutchinson and Mosier (1981) and the quadratic model explored by Wagner et al. (1997), were applied to NSS chamber observations, although both approaches are limited in their applicability or interpretation. For example, the physical significances of the fitted polynomial coefficients of the quadratic model are not necessarily either apparent or meaningful. In turn, the diffusion model advanced by Hutchinson and Mosier (1981) is compromised by its assumption of steady-state conditions at every point in time (Hutchinson and Mosier, 1981; Hutchinson and Livingston, 2002) and, as originally implemented, limited in its applicability (Anthony et al., 1995; Pedersen, 2000), although Pedersen (2000) and Pedersen et al. (2001)mathematically extended this model to permit its application to any number and spacing of observations with time and to reduce its sensitivity to measurement error. We refer hereafter to this approach as the H–M–P model. The non-steady-state diffusive flux estimator (NDFE) recently introduced by Livingston et al. (2005) is, to date, G.P. Livingston, Rubenstein School of the Environment and Natural Resources, and K. Spartalian, Dep. of Physics, Univ. of Vermont, Burlington, VT 05602; G.L. Hutchinson, USDA-ARS, Natural Resources Research Center, Fort Collins, CO. G.P. Livingston, current address: Altos Imaging, Hinesburg, VT 05461. Received 27 Sept. 2005. *Corresponding author ([email protected]). Published in Soil Sci. Soc. Am. J. 70:1459–1469 (2006). Soil Physics and Soil Biology & Biochemistry doi:10.2136/sssaj2005.0322 a Soil Science Society of America 677 S. Segoe Rd., Madison, WI 53711 USA Abbreviations: H–M–P, Hutchinson–Mosier–Pedersen; NDFE, nonsteady-state diffusive flux estimator; NSS, non-steady state. R e p ro d u c e d fr o m S o il S c ie n c e S o c ie ty o f A m e ri c a J o u rn a l. P u b lis h e d b y S o il S c ie n c e S o c ie ty o f A m e ri c a . A ll c o p y ri g h ts re s e rv e d . 1459 Published online August 3, 2006