Fluvial landscapes are dissected by channels, and at their upstream termini are channel heads. Accurate reconstruction of the fluvial domain is fundamental to understanding runoff generation, storm hydrology, sediment transport, biogeochemical cycling, and landscape evolution. Many methods have been proposed for predicting channel head locations using topographic data, yet none have been tested against a robust field data set of mapped channel heads across multiple landscapes. In this study, four methods of channel head prediction were tested against field data from four sites with high-resolution DEMs: slope-area scaling relationships; two techniques based on landscape tangential curvature; and a new method presented here, which identifies the change from channel to hillslope topography along a profile using a transformed longitudinal coordinate system. Our method requires only two user-defined parameters, determined via independent statistical analysis. Slope-area plots are traditionally used to identify the fluvial-hillslope transition, but we observe no clear relationship between this transition and field-mapped channel heads. Of the four methods assessed, one of the tangential curvature methods and our new method most accurately reproduce the measured channel heads in all four field sites (Feather River CA, Mid Bailey Run OH, Indian Creek OH, Piedmont VA), with mean errors of −11, −7, 5, and −24 m and 34, 3, 12, and −58 m, respectively. Negative values indicate channel heads located upslope of those mapped in the field. Importantly, these two independent methods produce mutually consistent estimates, providing two tests of channel head locations based on independent topographic signatures.

Mountain uplift and erosion have regulated the balance of carbon between Earth’s interior and atmosphere, where prior focus has been placed on the role of silicate mineral weathering in CO₂ drawdown and its contribution to the stability of Earth’s climate in a habitable state^1–5. However, weathering can also release CO₂ as rock organic carbon (OC_petro) is oxidized at the near surface^6,7; this important geological CO₂ flux has remained poorly constrained^3,8. We use the trace element rhenium in combination with a spatial extrapolation model to quantify this flux across global river catchments^3,9. We find a CO₂ release of $${68}_{-6}^{+18}$$68 − 6 + 18 megatons of carbon annually from weathering of OC_petro in near-surface rocks, rivalling or even exceeding the CO₂ drawdown by silicate weathering at the global scale¹⁰. Hotspots of CO₂ release are found in mountain ranges with high uplift rates exposing fine-grained sedimentary rock, such as the eastern Himalayas, the Rocky Mountains and the Andes. Our results demonstrate that OC_petro is far from inert and causes weathering in regions to be net sources or sinks of CO₂. This raises questions, not yet fully studied, as to how erosion and weathering drive the long-term carbon cycle and contribute to the fine balance of carbon fluxes between the atmosphere, biosphere and lithosphere^2,11.

For over a century, geomorphologists have attempted to unravel information about landscape evolution, and processes that drive it, using river profiles. Many studies have combined new topographic datasets with theoretical models of channel incision to infer erosion rates, identify rock types with different resistance to erosion, and detect potential regions of tectonic activity. The most common metric used to analyse river profile geometry is channel steepness, or k_s. However, the calculation of channel steepness requires the normalisation of channel gradient by drainage area. This normalisation requires a power law exponent that is referred to as the channel concavity index. Despite the concavity index being crucial in determining channel steepness, it is challenging to constrain. In this contribution, we compare both slope–area methods for calculating the concavity index and methods based on integrating drainage area along the length of the channel, using so-called chi (χ) analysis. We present a new χ-based method which directly compares χ values of tributary nodes to those on the main stem; this method allows us to constrain the concavity index in transient landscapes without assuming a linear relationship between χ and elevation. Patterns of the concavity index have been linked to the ratio of the area and slope exponents of the stream power incision model (m∕n); we therefore construct simple numerical models obeying detachment-limited stream power and test the different methods against simulations with imposed m and n. We find that χ-based methods are better than slope–area methods at reproducing imposed m∕n ratios when our numerical landscapes are subject to either transient uplift or spatially varying uplift and fluvial erodibility. We also test our methods on several real landscapes, including sites with both lithological and structural heterogeneity, to provide examples of the methods' performance and limitations. These methods are made available in a new software package so that other workers can explore how the concavity index varies across diverse landscapes, with the aim to improve our understanding of the physics behind bedrock channel incision.

Floodplain and terrace features can provide information about current and past fluvial processes, including channel response to varying discharge and sediment flux, sediment storage, and the climatic or tectonic history of a catchment. Previous methods of identifying floodplain and terraces from digital elevation models (DEMs) tend to be semi-automated, requiring the input of independent datasets or manual editing by the user. In this study we present a new method of identifying floodplain and terrace features based on two thresholds: local gradient, and elevation compared to the nearest channel. These thresholds are calculated statistically from the DEM using quantile–quantile plots and do not need to be set manually for each landscape in question. We test our method against field-mapped floodplain initiation points, published flood hazard maps, and digitised terrace surfaces from seven field sites from the US and one field site from the UK. For each site, we use high-resolution DEMs derived from light detection and ranging (lidar) where available, as well as coarser resolution national datasets to test the sensitivity of our method to grid resolution. We find that our method is successful in extracting floodplain and terrace features compared to the field-mapped data from the range of landscapes and grid resolutions tested. The method is most accurate in areas where there is a contrast in slope and elevation between the feature of interest and the surrounding landscape, such as confined valley settings. Our method provides a new tool for rapidly and objectively identifying floodplain and terrace features on a landscape scale, with applications including flood risk mapping, reconstruction of landscape evolution, and quantification of sediment storage and routing.

The concavity index, , describes how quickly river channel gradient declines downstream. It is used in calculations of normalized channel steepness index, , a metric for comparing the relative steepness of channels with different drainage area. It is also used in calculating a transformed longitudinal coordinate, , which has been employed to search for migrating drainage divides. A value of 0.45 is typically assumed in studies. Here we quantify the variability in across multiple landscapes distributed across the globe. We describe the degree to which both the spatial distribution and magnitude of and can be distorted if is assumed rather than constrained. Differences between constrained and assumed of 0.1 or less are unlikely to affect the spatial distribution and relative magnitude of values, but larger differences can change the spatial distribution of and in extreme cases invert differences in relative steepness: relatively steep reaches can appear relatively gentle as quantified by . These inversions are function of the range of drainage area in the considered watersheds. We also demonstrate that the coordinate, and therefore the detection of migrating drainage divides, is sensitive to varying values of . The median of most likely across a wide range of mountainous and upland environments is 0.425. This wide range of variability suggests workers should not assume any value for , but should instead calculate a representative for the landscape of interest, and exclude basins for which this value is a poor fit.

Drainage density is a fundamental landscape metric describing the extent of the fluvial network. We compare the relationship between drainage density (D_d) and erosion rate (E) using the Channel-Hillslope Integrated Landscape Development (CHILD) numerical model. We find that varying the channel slope exponent (n) in detachment-limited fluvial incision models controls the relationship between D_d and E, with n > 1 resulting in increasing D_d with E if all other parameters are held constant. This result is consistent when modeling both linear and nonlinear hillslope sediment flux. We also test the relationship between D_d and E in five soil-mantled landscapes throughout the USA: Feather River, CA; San Gabriel Mountains, CA; Boulder Creek, CO; Guadalupe Mountains, NM; and Bitterroot National Forest, ID. For two of these field sites we compare D_d to cosmogenic radionuclide (CRN)-derived erosion rates, and for each site we use mean hilltop curvature as a proxy for erosion rate where CRN-derived erosion rates are not available. We find that there is a significant positive relationship between D_d, E, and hilltop curvature across every site, with the exception of the San Gabriel Mountains, CA. This relationship is consistent with an n exponent greater than 1, suggesting that at higher erosion rates, the transition between advective and diffusive processes occurs at smaller contributing areas in soil-mantled landscapes.