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Despite its environmental and scientific significance, predicting gully erosion remains problematic. This is especially so in strongly contrasting and degraded regions such as the Horn of Africa. Machine learning algorithms such as random forests (RF) offer great potential to deal with the complex, often non‐linear, nature of factors controlling gully erosion. Nonetheless, their applicability at regional to continental scales remains largely untested. Moreover, such algorithms require large amounts of observations for model training and testing. Collecting such data remains an important bottleneck. Here we help to address these gaps by developing and testing a methodology to simulate gully densities across Ethiopia, Eritrea and Djibouti (total area: 1.2 million km2). We propose a methodology to quickly assess the gully head density (GHD) for representative 1 km2 study sites by visually scoring the presence of gullies in Google Earth and then converting these scores to realistic estimates of GHD. Based on this approach, we compiled GHD observations for 1,700 sites. We used these data to train sets of RF regression models that simulate GHD at a 1 km2 resolution, based on topographic/geomorphic, land cover, soil and rainfall conditions. Our approach also accounts for uncertainties in GHD observations. Independent validations showed generally acceptable simulations of regional GHD patterns. We further show that: (i) model performance strongly depends on the amount of training data used, (ii) large prediction errors mainly occur in areas where also the predicted uncertainty is large and (iii) collecting additional training data for these areas results in more drastic model performance improvements. Analyses of the feature importance of predictor variables further showed that patterns of GHD across the Horn of Africa strongly depend on NDVI and annual rainfall, but also on normalized steepness index (ksn) and distance to rivers. Overall, our work opens promising perspectives to assess gully densities at continental scales. © 2020 John Wiley & Sons, Ltd.

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Gully erosion is a particularly damaging process which is not yet sufficiently understood and parameterized. Gully head topographic threshold relative to Hortonian runoff have been studied in cropland, rangeland and forest. This study extends such modelling approach to badlands. Different badlands (eight sites) have been studied in the Mediterranean environment in Italy and Spain, characterized by diversified climatic, lithological, and geological settings under different anthropogenic conditioning. Many badlands have been characterized by their specific human history in addition to their geomorphological properties. Land use, as part of the human history, strongly affected many badland formation and development, through extremely impacting land exploitation (usually overgrazing). The effect of geological and geomorphological processes are usually particularly well visible. While the weakening effect of joints is confirmed, the different geological layer bedding orientation with respect to the slope aspect generates a different development of badland morphologies and different values of gully head thresholds values (as shown in two badlands sites on the same geological material and climate.The selection of Curve Number values, at the base of the introduction of land use into the gully head thresholds, has been more objectively defined in order to reduce arbitrariness in threshold application. The study additionally revises some of the physical basics behind the gully head threshold concept, requiring a description of the soil resistance in terms of frictional and cohesive components. This implies the explicit inclusion of rock fragment into the grain size distribution, which cannot be limited to fine grains. It results into an enriched threshold formulation that allows to describe the condition for gully head initiation and retreat as the result of the tradeoff between the frictional and cohesive components of the soil resistance forces.Eventually, the gully head threshold concept is confirmed and extended to include badlands.

<p>Gully erosion has been recognized as a main driver of soil erosion and land degradation. While numerous studies have focussed on understanding gully erosion at local scales, we have very little insights into the patterns and controlling factors of gully erosion at a global scale. Overall, this process remains notoriously difficult to simulate and predict. A main reason for this is that the complex and threshold-dependent nature of gully formation leads to very high data requirements when aiming to simulate this process over larger areas.</p><p>Here we help bridging this gap by presenting the first data-driven analysis of gully head densities at a global scale.  We developed a grid-based scoring method that allows to quickly assess the range of gully head densities in a given area based on Google Earth imagery. Using this approach, we constructed a global database of mapped gully head densities for currently >7400 sites worldwide. Based on this dataset and globally available data layers on relevant environmental factors (topography, soil characteristics, land use) we explored which factors are dominant in explaining global patterns of gully head densities and propose a first global gully head density map.</p><p>Our results indicate that there are ca. 1.7 to 2 billion gully heads worldwide. This estimate might underestimate the actual numbers of gully heads since ephemeral gullies (in cropland) and gullies under forest remain difficult to map. Our database and analyses further reveal clear regional patterns in the presence of gullies. Around 27% of the terrestrial surface (excluding Antarctica and Greenland) has a density of > 1 gully head/km², while an estimated 14% has a density of > 10 gully heads/km² and 4% has even a density of > 100 gully heads/km². Major hotspots (with > 50 gully heads/km²) include the Chinese loess plateau, but also Iran, large parts of the Sahara Desert, the Andes and Madagascar. In addition, gully erosion also frequently occurs (with typical densities of 1-50 gully heads/km²) in the Mid-West USA, the African Rift, SE-Brazil, India, New-Zealand and Australia.</p><p>These regional patterns are mainly explained by topography and climate in interaction with vegetation cover. Overall, the highest gully densities occur in regions with some topography and a (semi-)arid climate. Nonetheless, it is important to point out that not all gully heads are still actively retreating. Building on earlier insights into the magnitude and controlling factors of gully head retreat rates, we explore what our current results imply for assessing actual gully erosion rates at a global scale.</p>