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Response to Comment on “In-Stream Nitrogen Attenuation: Model-Aggregation Effects and Implications for Coastal Nitrogen Impacts” We thank Alexander, Smith, and Schwarz (1) for the interest and attention given to our paper (2). The study (2) compared calculated first-order Nitrogen (N) attenuation rates kcell on a relatively fine POLFLOW model resolution scale of uniform 1 × 1 km2 grid cells with similarly defined rates ksc calculated from the same model results for different larger subcatchment resolution scales. Average values of ksc differed from those of kcell and exhibited a stream-depth dependence, which kcell did not. The difference was a model aggregation/ resolution artifact because such model differences were the only ones involved between the ksc and kcell calculations. This leads clearly to our main conclusion (2) that “spatial model aggregation may lead to artificial decrease of calibrated nitrogen loss rates with increasing stream depth (or flow), in addition to any such dependences that may prevail in independently measurable reality.” This conclusion is general to all model studies that may calculate first-order N attenuation rates on some chosen model resolution scale and from them draw general conclusions about real rate behavior, without quantitative investigation of possible model resolution artifacts. Our paper (2) made no claim to describing the underlying reality of N attenuation rates, but only to showing that this reality may appear to us differently for different subjective model resolution choices. Previous SPARROW-based studies came into particular focus in this context because they explicitly calibrated first-order N attenuation rates for entire stream reaches and presented their obtained stream-depth dependence as general reality without any reported quantification of possible model resolution effects. Besides comparative illustration of cited previous SPARROW results, there is nowhere in our paper (2) any mention or use of any new simulation results produced by or attributed to SPARROW, so discussions in the comment (1) about alleged erroneous SPARROW model attributions in the original publication (2) are irrelevant. The N attenuation rates kcell and ksc (2) are simply and consistently quantified from the same model (POLFLOW) results on N transport and attenuation as kcell ) -ln(Mout,cell/ Min,cell)/Tcell and ksc ) -ln(Mout,sc/Min,sc)/Tsc, where Mout,cell and Min,cell are the modeled N output and input mass, respectively, for each POLFLOW model grid cell, Tcell is N travel time through the same cell, and Mout,sc, Min,sc, and Tsc are the analogous quantities for the aggregation of grid cells that makes up each considered sub-catchment. Considered sub-catchments (2) were incremental sub-catchments identified by the Swedish Meteorological and Hydrological Institute (SMHI) as being management-relevant. The subcatchment N mass measure Min,sc was simply obtained by summing up all modeled Min,cell values for all the cells that constitute each sub-catchment, Mout,sc was the N mass output at the outlet of each sub-catchment and Tsc was estimated from the empirical equation Tsc ) (-0.0065 + 0.2642A0.3)/2. Figure 1a shows that this Tsc estimate is smaller than (more or less about half) the maximum advective solute travel time through entire sub-catchments, as obtained by directly imax+Ncellmax i summing up cell travel times Tmax Tcell, where sc ) ∑i)imax max Ncell is the total number of downstream cells along the mean flow direction from cell imax at the upstream boundary origin to the sub-catchment outlet. Figure 1b shows an alternative 10.1021/es060112b CCC: $33.50 Published on Web 02/24/2006
2006 American Chemical Society
FIGURE 1. Comparison of different expressions of solute travel time and N attenuation rate in (sub)catchments. (a) Empirical travel time expression Tsc and maximum Tmax sc value of advective solute travel time in sub-catchments with different surface areas up to the entire Norrstro1 m basin. (b) Average N attenuation rate at the grid cell scale, kcell (thick solid line) compared with average subcatchment N attenuation rate ksc as given from the different travel time measures Tsc and maximum Tmax for different stream-depth sc classes. Mean stream depth is obtained as in ref 4 from D ) 0.2612q0.3966, with q being cell-specific streamwater flow obtained from the POLFLOW water flow module for kcell calculations, and (sub)catchment-averaged streamwater flow for ksc calculations. comparison between kcell and ksc to that presented in ref 2, using here consistently for both N attenuation rate quantifications solute travel times 0.5Tcell and 0.5Tmax sc , i.e., half the maximum travel time through the respective resolution scale unit (cell or sub-catchment), with also slightly different subcatchment definitions than in ref 2, as given from the digital elevation maps used for assigning streamflow directions in the POLFLOW model (instead of the SMHI definitions). Figure VOL. 40, NO. 7, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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1b illustrates for comparison also the ksc quantification obtained for the new sub-catchment definitions by the same empirical travel time estimate Tsc as in ref 2. In contrast to the qualitative discussions in the comment (1), Figure 1b shows quantitatively that the main conclusion of our original publication (2) remains valid and general for different possible measures of sub-catchment travel time and sub-catchment definitions. The new sub-catchment definitions are more consistent with the POLFLOW modeling approach than the SMHI definitions used in ref 2 and retain the artificial stream-depth dependence result for large-scale ksc while reproducing the prediction of the earlier analytical study by Lindgren and Destouni (3) that large-scale ksc will mostly underestimate smaller-scale kcell data; however, (3) predicted also that ksc may overestimate kcell under certain conditions, so results in ref 2 were in no principle contradiction.
Literature Cited (1) Alexander, R. B.; Smith, R. A.; Scharwz, G. E. Comment on “In-stream nitrogen attenuation: Model-aggregation effects
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and implications for coastal nitrogen impacts”. Environ. Sci. Technol. 2006, 40, 2485-2486. (2) Darracq, A.; Destouni, G. In-stream nitrogen attenuation: Model-aggregation effects and implications for coastal nitrogen impacts. Environ. Sci. Technol. 2005, 39, 3716-3722. (3) Lindgren, G. A.; Destouni, G. Nitrogen loss rates in streams: Scale-dependence and up-scaling methodology. Geophys. Res. Lett. 2004, 31, L13501. (4) Alexander, R. B.; Smith, R. A.; Schwarz, G. E. Effect of stream channel size on the delivery of Nitrogen to the Gulf of Mexico. Nature 2000, 403, 758-761.
Georgia Destouni, and Ame´ lie Darracq Department of Physical Geography and Quaternary Geology Stockholm University SE-106 91, Stockholm, Sweden ES060112B
