“…An alternative approach for estimating R that reduces estimation noise and avoids the risk of overfitting is to choose R on a finite spatiotemporal grid ("fitting grid"), such that the corresponding predicted distribution Ĉ obtained by solving the differential Equation (6) best matches the observed profile C. This approach, known as "inverse linear transport modeling" (ILTM), is widely used in oceanography and atmospheric sciences, where known distributions of compounds are used to estimate unknown sources and sinks (Berg et al, 1998;Hirsch et al, 2006;Houweling, Kaminski, Dentener, Lelieveld, & Heimann, 1999;Lettmann et al, 2012;Louca et al, 2016;Martinez-Camara, Béjar Haro, Stohl, & Vetterli, 2014;Mikaloff Fletcher et al, 2006Steinkamp, 2011). We mention that most existing studies-including those investigating metabolite fluxes in anoxic water columns or sediments (Berg et al, 1998;Lettmann et al, 2012;Louca et al, 2016)-assumed that C was at steady state even when fluxes were estimated at multiple time points; however, this assumption may be needlessly and overly restrictive. To reduce spurious oscillations in the estimated R (a common ILTM artifact), excessively high estimates of R that only marginally improve the agreement with the data are penalized, a procedure known as Tikhonov regularization (Björck, 1996;Hansen, 2000;Lettmann et al, 2012).…”