Comment on ‘‘Power law catchment-scale recessions arising from heterogeneous linear small-scale dynamics’’ by

[1] It is demonstrated that a near-linear subsurface runoff response from a short and relatively steep slope segment and a nonlinear response at the watershed scale may primarily arise from geometry rather than from an assumed linear nature of the subsurface runoff response from the hillslope, as Harman et al. [2009] employed for the Panola Mountain Research (PMR) catchment in Georgia. The authors caution in their paper that hydraulic theory (exemplified by the study of Brutsaert and Nieber [1977]) cannot generally account for the heterogeneity in the watershed scale and therefore should be used with certain reservation when employing it for catchment-scale parameter estimation. They base this on observations [Clark et al., 2009] that the PMR watershed in Georgia displays a near-linear (which Harman et al. accept to be linear) subsurface flow response at a short segment ( 50 m) of the upper part of a hillslope, while the same response becomes increasingly nonlinear with scale. The authors employ linear reservoirs in parallel, with prescribed distributions (e.g., bounded power law (BPL)) of the storage coefficient and in the limit; when the number of reservoirs approaches infinity, they obtain the required degree of nonlinearity in their summed outflow. With the application of the BPL distribution, the shape of which changes significantly with scale, they can achieve the observed full range and temporally changing nature of the exponent of the recession flow equation. This way, they argue that the nonlinear subsurface flow response from the PMR watershed may emerge from a combination of linear responses similar to what is observed at the short upslope segment. [2] The logic behind the parallel reservoir approach taken by Harman et al. [2009] is this: an observed near-linear subsurface runoff response from a short, relatively steep uphill portion of a hillslope leads to the assumption of a linear response for all hillslopes within the catchment. However, to my best knowledge such a general linear hillslope response in the PMR watershed was never observed, since hillslope runoff measurements were taken only at one particular short uphill slope segment. This then questions the suitability of employing a linear reservoir for the description of the general hillslope response and, consequently, that of the watershed. [3] With the help of the 2-D combined Richards equation an alternative explanation of the seemingly different subsurface runoff response between the short uphill segment and the watershed is presented here, acknowledging that reality is certainly much richer than what is captured in the ensuing brief and highly simplified modeling. As described by Freer et al. [2002], subsurface flow response at the hillslope was obtained in a trench running perpendicular to the slope gradient and dug down to the rock surface. This latter property is important because, this way, the slope section (and its subsurface flow dynamics) uphill of the trench is cut off from the rest of the slope downhill and the trench acts as a drain. Therefore, in comparison with the typical watershed hillslope, one has a short, relatively steep hillslope with relatively thin soil, and, because it is an uphill segment, it receives relatively little support from surface and subsurface flow from above. In addition, the resulting subsurface outflow is collected and removed, thus creating zero water levels in the trench, which is also somewhat different from the case of the typical slope of the catchment that is drained at least intermittently by a stream with nonzero water depth. This last difference from the ensuing modeling point of view is, however, minor since, having no information of whether the streams at the catchment are fully or partially incised, they will be assumed to be fully penetrating here with zero stream water depth (h = 0) for the trench and a constant nonzero depth for the typical watershed. [4] Having a look at the map of the watershed [Clark et al., 2009], it is safe to assume a magnitude difference of the specific hillslope segment length mentioned above and that of the average hillslope of the catchment. Let us then consider two slopes now, one with a base length of 20 m, a slope of 1:2, and a soil thickness of 0.5 m, drained by a fully incised stream with zero stream levels. Let the other slope have a base length of 200 m, a slope of 1:10, and a soil thickness of 1 m, drained by a fully incised stream with h = 0.1 m (Figure 1). Let both slopes be covered by soils of a loam-type physical texture as described by Szilagyi et al. [2008]. Because the shorter slope is steeper and because it has less moisture support from above (in the form of, for example, interflow and/or preferential flow and surface runoff with the ensuing enhanced infiltration) than the longer one, let it have full saturation up to a unit height from its base only, while the longer one will have saturation up to 10 m (Figure 1), before drainage simulations start. Department of Hydraulic and Water Resources Engineering, Budapest University of Technology and Economics, Budapest, Hungary. Also at School of Natural Resources, University of Nebraska at Lincoln, Lincoln, Nebraska, USA.