Drainage reorganization disrupts scaling between drainage area and valley width

Valley width is a fundamental morphologic property of rivers that plays a key role in drainage networks' hydrology, ecology, and geomorphology. In many cases, defining and measuring valley width is far from trivial. Therefore, similar to channel width, the valley width (W) is commonly approximated as a power law function of the drainage area (A) and expressed as W = k_cA^d. Global observations have shown that the exponent  (d) can vary widely but is typically ~0.5. However, in fluvial systems that have undergone drainage reorganization, gradual or abrupt changes in drainage areas along the valley could produce widths that are disproportionate to their drainage areas. As a result, the valley width - drainage area relationship in reorganized systems is expected to differ from undisturbed drainages that have not undergone reorganization.

To test this prediction, we studied 12 valleys in the Negev desert, Israel, and classified them into three categories, based on field evidence and remote sensing data: (i) undisturbed valleys, which are minimally affected by reorganization; (ii) beheaded valleys, whose headwaters were beheaded; and (iii) reversed valleys, which have reversed their flow direction by 180 degrees while exploiting their antecedent valleys. Using a new semi-automatic tool to measure valley width on high-resolution DEMs, we calibrated the best-fit power law for each valley to explore the relationships between drainage area and valley width for each valley category.

Our results show that the valley width-drainage area scaling in reorganized valleys deviated significantly from those in undisturbed valleys in our field area and global observations. The drainage area exponents (d) were lower in beheaded valleys compared to undisturbed valleys but remained positive. In contrast, reversed valleys were characterized by negative d exponents, indicating valley width decrease with increasing drainage area. For the reversed category, we also explored the independent effect of channel slope (S), where the valley width is W = k_b A^bS^c, which resulted in negative and overall similar values of b and c.

In one reversed valley section, we compared the scaling of valley versus channel width as a function of drainage area. We found that in contrast to the downstream narrowing valley, the channel width shows an opposite trend and widens downstream, suggesting that the channel has mostly adjusted to the post-reorganization drainage area distribution. The narrow reversed channel shapes the width of the formative flows, which contrasts significantly with the wide 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 further divide migration.

Our findings can be used to identify landscapes that have been affected by recent drainage reorganization and should be taken into consideration in studies that use the relationship between valley width and drainage area for valley width predictions, stream power calculations, and landscape evolution models.