## 1. Introduction

[2] Recession flows are characterized by continuously decreasing streamflow over time occurring during dry or no-rain periods. Drainage basins, irrespective of their location and size, follow an interesting recession flow pattern that –*dQ*/*dt* and *Q* (*Q* being discharge at the outlet at time *t*) exhibit a power law relationship [*Brutsaert and Nieber*, 1977]:

[3] *Biswal and Marani* [2010] suggested that recession flow in a basin is controlled by the dynamics of its active drainage network or ADN (the part of the drainage network that is actively draining at time *t*). In particular, they hypothesized that the gradual shrinking of the ADN [see, e.g., *Gregory and Walling*, 1968; *Blyth and Rodda*, 1973; *Day*, 1983] originates the power law relationship between –*dQ*/*dt* and *Q* (equation (1)). In order to prove their hypothesis, they proposed a conceptual model, the geomorphological recession flow model (GRFM), by making two simple assumptions that during a recession event: (i) the rate of flow generation per unit ADN length (*q*) remains constant in both space and time and (ii) the speed at which the heads of the ADN configuration move downstream (*c*) also remains constant in both space and time. With these two assumptions, one can find that the power law exponent α in equation (1) is equal to the power law exponent of the *N*(*t*) versus *G*(*t*) curve [*Biswal and Marani*, 2010], where *N*(*t*) and *G*(*t*) are, respectively, the number of heads and the total length of the ADN configuration at time *t*. Note that as *c* is constant, *t* = *l/c*, *l* being the distance of any ADN head from its farthest source or channel head at time *t*. Because of the linear relationship between *l* and *t*, both the *N*(*t*) versus *G*(*t*) curve and the *N*(*l*) versus *G*(*l*) curve give the same power law exponent, the geomorphic α (α* _{g}*). Thus, α

*depends only on the structure of the channel network, an entity that remains unchanged over time.*

_{g}[4] *Biswal and Marani* [2010] observed that –*dQ*/*dt* versus *Q* curves from a basin can be different for different recession events, which implies that α must be computed individually for the available recession curves. They then considered the median of the distribution of the α values as the representative α (α* _{r}*) of the basin, as the distribution is often skewed. Considering streamflow data from 67 basins situated across the United States, they found that α

*is nearly equal to 2, particularly when the basins are steep and free from significant human interventions (see also*

_{r}*Shaw and Riha*[2012]). Then they used digital elevation models (DEMs) for the same set of basins and found that their α

*values are nearly equal to 2.1. The observation α*

_{g}*being nearly equal to α*

_{r}*, or the error*

_{g}*ϵ*(α

*− α*

_{r}*) being nearly equal to zero, implies that the assumptions made by the GRFM (both*

_{g}*q*and

*c*remain constant during a recession event) are adequate for the majority of recession events in a basin. However, the GRFM does not explain why some recession events do not give α equal to α

*. Also, it was found that some natural basins display large*

_{g}*ϵ*values (see the inset of Figure 4,

*Biswal and Marani*[2010]). We propose that, when observational errors are negligible, α deviates from α

*because either*

_{g}*q*or

*c*, or both vary during the recession event.

[5] In this study, we propose a broader theoretical framework to explain the deviation of observed α from α* _{g}* by allowing both

*q*and

*c*to vary along stream channels. First, we reformulate the GRFM in the context of Horton-Strahler tree networks. We then generalize the model by expressing both

*q*and

*c*as functions of Horton-Strahler stream order. We show that the constant

*q*and constant

*c*assumptions, as adopted by the GRFM, are not the necessary conditions for having α =α

*. We then analyzed observed recession curves from 39 U.S. Geological Survey (USGS) basins and found that there exists a power law relationship between α and the recession flow curve peak. Our analysis attempts to explain how the variation in subsurface storage distribution across streams of different orders controls the value of α.*

_{g}