On the variability of the exponent in the power law depth dependence of POC flux estimated from sediment traps

Using the power law relationship J(z)=J0(z/z0)-b relating the particulate organic carbon (POC) flux in the water column at depth z to the export flux J0 at z0=100m, I reanalyzed the sediment-trap data set compiled by Berelson [2001. The flux of particulate organic carbon into the ocean interior: a comparison of four U.S. JGOFS regional studies. Oceanography 14, 59-67]. The goal is to better understand the variability of the exponent b. I show that the usual approach of estimating parameters for each station separately and then pooling the estimates from all stations confounds within-station estimation errors with true regional variability and so tends to inflate the apparent variance of b. Furthermore, I show that the correlation between b and J0 observed by Berelson [2001. The flux of particulate organic carbon into the ocean interior: a comparison of four U.S. JGOFS regional studies. Oceanography 14, 59-67] is spurious and attributable to the fact that the estimation errors for b and J0 are correlated. A two level mixed-effects regression model is introduced to properly take into account the contribution to the variability of the POC fluxes of within- and between-station effects. The analysis shows that the variability of b across stations is only a small contributor to the POC flux variance in the sediment trap data set. In fact the additional POC flux variance captured by a model with regionally varying b in comparison to a simple model with a fixed b is not statistically significant. The best estimate for the fixed b applicable to all stations is 0.70±0.08 (95% C.I. 90 d.f.).