Reply to comment by Richard M. Iverson on “Piezometric response in shallow bedrock at CB1: Implications for runoff generation and landsliding”

Abstract

[1] Iverson [2004] has offered a useful commentary on our paper, and we appreciate this opportunity to offer corrections and to raise some important questions. The issue he raises deals with a subsidiary part of the paper, and none of our primary conclusions are affected by these corrections. [2] Iverson [2000] proposed a useful scaling argument for understanding the relative role in pore pressure development during a rainstorm of lateral flow from upslope contributing areas versus slope normal flow. He suggests that the ratio A/D0 ‘‘approximates the minimum time necessary for strong lateral pore pressure transmission from the area A to the point (x, y, H),’’ whereas H/D0 ‘‘approximates the minimum time necessary for strong slope-normal pore pressure transmission from the ground surface to depth H.’’ Iverson argues that A must be approximated by ‘‘some readily measurable property’’ and states that A is ‘‘the area enclosed by the upslope topographic divide and hypothetical flow lines that run normal to topographic contours and bound the region that can contribute surface runoff to point (x, y).’’ Iverson defines D0 as the ‘‘maximum characteristic diffusivity’’ given by the ratio of saturated conductivity (Ksat) to C0, the minimum value of C(y) defined as ‘‘the change in volumetric water content per unit change in pressure head’’ (i.e., C(y) = dq/dy, where q is the volumetric water content and y is pressure head). Iverson introduces D0 to give a useful ‘‘reference time’’ and argues that comparison of these two timescales demonstrates that the ‘‘slope-normal’’ component must control slope instability because it delivers a pore pressure response much quicker. We argued in this article, and in our previous reports on our study site [Torres et al., 1998; Montgomery and Dietrich, 2002] that rapid pore pressure response that controls both slope instability and general hydrologic response is driven by vertical flow, not lateral flow. Hence there is no disagreement between Iverson and us on this important finding. We both agree, too, that the lateral flow contribution is, nonetheless, important in that it affects the ‘‘propensity for landsliding’’ [Iverson, 2000] because it strongly influences the pore pressure field antecedent to a burst of rain that could initiate a landslide. [3] Iverson correctly points out that we miscalculate D0. Instead, we mistakenly calculated the dimensionally equivalent transmissivity (saturated conductivity times depth), which we often use in subsurface runoff modeling. There is no point in clarifying how we arrived at our estimated timescales for site response, as they were based on an erroneous definition and are simply wrong. Old habits sometimes blind one, and we are thankful that Iverson caught this foolish mistake. [4] There are, however, some issues in regard to the application of Iverson’s scaling ratios to the Coos Bay data that are worth reviewing. In his comment, Iverson argues that an effective depth-averaged dq/dy for the wet region (q > 0.2) of the soil-water retention curve of Coos Bay soil is about 0.1 m . The soil water retention curves of Coos Bay soils are strongly nonlinear, such that while not ‘‘at saturation’’ small changes in y require large changes in q as the pressure head nears zero, but before the soil reaches saturation. Torres et al. [1998, Figure 5] show that soil tensions were nearly all less than 0.1 m in response to irrigation, and a median value of about 0.03 m typified the pressure head for wet conditions. The values of dq/dy for the change in y between 0.1 and a ‘‘hinge’’ beyond which dq/dy increases greatly as y approaches 0 for the six soil water retention curves reported by Torres et al. [1998] for CB1 range from 0.1 to 0.7 m , or up to seven times the value assumed by Iverson. For winter conditions when landslides are most likely, y will be near zero and the soil moisture retention curves for CB1 [Torres et al., 1998] show that dq/dy may be even larger. This means that D0, assuming Ksat of 10 4 m s , is from 10 3 m s 1 to a value of 1.4 10 4 m s , 7 times smaller than assumed by Iverson [2000, Table 1]. Using these values of D0, H /D0 ranges from about 20 min to 1.9 hr for a 1 m thick soil, and from 1.1 to 7.8 hr for a 2 m thick soil due to the squared dependency on soil depth. Copyright 2004 by the American Geophysical Union. 0043-1397/04/2003WR002815$09.00