HR: 11:45h
AN: U52A-08    [Abstracts]
TI: Temporal Scaling of Biogeochemical Reaction Rates
AU: * Rothman, D H
EM: dhr@mit.edu
AF: Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, United States
AU: Forney, D C
EM: dforney@MIT.EDU
AF: Department of Mechanical Engineering and Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, United States
AB: In at least two disparate areas of organic and inorganic geochemistry---the microbial degradation of detritus and the dissolution of minerals in sediments and soils---apparent rate constants k have been observed to diminish with the "age" t of the substrate like k(t) ~eq a t^-b, where a ~eq 0.2 and b ~eq 1.0. Published reports display up to ten orders of magnitude in time [1,2]. Because the accuracy of biogeochemical models typically depends crucially on the specification of such rates, an understanding of this scaling law has important implications for predicting the evolution of biogeochemical cycles, especially the cycles of carbon and oxygen. The power-law decay of rates likely derives from a combination of chemical and physical heterogeneity. In a purely chemical scenario, an intrinsically heterogeneous substrate (e.g., a mixture of organic matter ranging from "labile" to "recalcitrant") is assumed to produce the observed slowdown of k(t). In contrast, a physical model assumes a homogeneous substrate in which rates nevertheless vary microscopically due to spatially varying physical constraints. Here we consider the extreme case of a purely physical origin and test its consistency with observations [3]. We first show how a diffusion-limited reaction-diffusion system leads to a logarithmic decay of the substrate. We then show how the power-law for k(t) derives from this logarithmic decay. We obtain not only the correct exponent b=1 but also a good approximation of the prefactor a. By constructing an extensive database of previously published measurements, we show that observations compare well to predictions. The particular way in which diffusion-limitation manifests itself varies from problem to problem. In the case of detrital decay in sediments, we suggest that rates are limited by contact of substrate with extracellular enzymes [3]. Mechanisms in soils are likely similar. For mineral dissolution is sediments, we suggest that rates are limited by diffusion of reactants from the seafloor. [1] J.~J.~Middelburg, Geochim.~Cosmochim.~Acta 53, 1577 (1989). [2] K.~Maher, D.~J.~DePaolo, J.~C.-F.~Lin, Geochim.~Cosmochim.~Acta 68, 4629. [3] D.~H.~Rothman and D.~C.~Forney, Science 316, 1325 (2004).
DE: 0414 Biogeochemical cycles, processes, and modeling (0412, 0793, 1615, 4805, 4912)
DE: 1051 Sedimentary geochemistry
DE: 4273 Physical and biogeochemical interactions
DE: 4475 Scaling: spatial and temporal (1872, 3270, 4277)
DE: 4806 Carbon cycling (0428)
SC: Union [U]
MN: 2007 Fall Meeting