Galster et al. (2006) use questionable data for two Pennsylvanian streams to misconstrue the dependence of streamflow on watershed area and urbanization. Their first equation, Q = kAc, relates flow rate ‘Q’ (m3/s) to drainage area ‘A’ (m2), using ‘k,’ “a measure of river base flow (m/s)” and ‘c’, “the scaling power dependency” (Galster, et al., 2006, p. 713) Their Table 3 reports both positive and negative values for k, and redefines its units as m3/s. Instead, Equation 1 requires that k be positive because both Q and A are positive, and that k has inconsistent units that depend on c. Because Table 3 reports that c ranges from 0.32 to 1.61 for different hydrographs in Sacony Creek (cf. Figure 1), k's units must vary from m+2.36/s to m−0.22/s. Such implausible and inconsistent units are one of many problems that arise when empirical relationships and log-log plots are misused in hydrology.
The values Galster et al. list for k in Table 3, e.g., −2.25 to +1.37 for Sacony Creek, actually are values of log k. Because the scale is logarithmic, this represents a >4,000 fold range for k, rendering it useless as a measure of base flow. Also, the various fits of Equation 1 to their data are poor and conflicting (Figure 1).
Dates of occurrence are not reported for most discharge events used by Galster et al., and when they are, inconsistencies abound. Their Figure 2 caption states that the results are for “December 2004 to January 2005,” yet their x-axis encompasses only June and July, 2005. None of the points shown in Figure 2 correspond in any way to Table 3, which is referenced in the caption. Worse, of the three hydrographs in Figure 2, the two for “Kutztown” and “Virginville” are impossibly identical.
Galster et al.'s conclusions can be tested by comparing sites along Little Lehigh (Rt. 100) and Sacony Creeks (Kutztown) that have comparable drainage areas (see their Table 3). The five “peak flows” reported in Table 3 for the Rt. 100 site range only from 0.59 to 1.03 m3/s, while the three peaks reported for Kutztown are much larger, at 11.62, 2.78, and 19.33 m3/s. Similarly, a huge difference arises when data for the 132 km2 catchment above the “Mill Creek” site in the Little Lehigh Creek watershed are compared with those for the 126 km2 “Game land” site in Sacony Creek. The three flow peaks reported for Mill Creek are only 1.88, 1.52, and 7.45 m3/s, while those for Game land are much larger on average, ranging from 4.14 to 84.01 m3/s. These examples suggest that peak flows for similarly sized rural parts of two adjacent watersheds typically differ by ~10x, which is not plausible, and are greatest for the “most natural” watershed, which runs counter to common sense and to the conclusions of Galster et al.
Finally, robust data sets do not support the contention of Galster et al. that c can exceed unity (e.g., Costa, 1987a, 1987b). Our Figure 2 shows the relationship between mean or record flow and basin area for 550 gaging stations in Pennsylvania (USGS, 2006). The regression line between mean discharge and area has a unit slope, as expected, and indicates that the average runoff for Pennsylvania is close to 50 cm/yr. The slope for record flows is ~0.79, a value that would correspond to c in Galster's Equation 1. No evidence is seen for steep slopes of ~1.8 as estimated by Galster et al. If real, their steep slope could only reflect the monotonic downstream increase in the percentage of impervious area in this particular watershed (their Fig. 3). This is a special case, because an otherwise identical watershed with the same impervious area, distributed differently, would not show such a slope. More likely, the high slope of 1.8 is an artifact that reflects an inappropriate combination of discharge determined by the U.S. Geological Survey and Galster et al., inaccurate peak flow estimations, or the different equations (exponential versus polynomial) used to calibrate the various rating curves.