Drainage reorganization induces deviations in the scaling between valley width and drainage area

The width of valleys and channels affects the hydrology, ecology, and geomorphic functionality of drainage networks. In many studies, the width of valleys and/or channels (W) is estimated as a power-law function of the drainage area (A), WCombining double low linekcAd. However, in fluvial systems that experience drainage reorganization, abrupt changes in drainage area distribution can result in valley or channel widths that are disproportional to their drainage areas. Such disproportionality may be more distinguished in valleys than in channels due to a longer adjustment timescale for valleys. Therefore, the valley width-area scaling in reorganized drainages is expected to deviate from that of drainages that did not experience reorganization. To explore the effect of reorganization on valley width-drainage area scaling, we studied 12 valley sections in the Negev desert, Israel, categorized into undisturbed, beheaded, and reversed valleys. We found that the values of the drainage area exponents, d, are lower in the beheaded valleys relative to undisturbed valleys but remain positive. Reversed valleys, in contrast, are characterized by negative d exponents, indicating valley narrowing with increasing drainage area. In the reversed category, we also explored the independent effect of channel slope (S) through the equation WCombining double low linekbAbSc, which yielded negative and overall similar values for b and c. A detailed study in one reversed valley section shows that the valley narrows downstream, whereas the channel widens, suggesting that, as hypothesized, the channel width adjusts faster to post-reorganization drainage area distribution. The adjusted narrow channel dictates the width of formative flows in the reversed valley, which contrasts with the meaningfully wider formative flows of the beheaded valley across the divide. This difference results in a step change in the unit stream power between the reversed and beheaded channels, potentially leading to a "width feedback"that promotes ongoing divide migration and reorganization. Our findings demonstrate that valley width-area scaling is a potential tool for identifying landscapes influenced by drainage reorganization. Accounting for reorganization-specific scaling can improve estimations of erosion rate distributions in reorganized landscapes.