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• Influence of soil properties on rill erosion is not adequately considered. • Study of timely changes in rill morphology and flow require advanced techniques. • Rill network requires more investigations to help prevent erosion at large scales. • Controlled experiments are case-specific and should be systematically integrated. • Rill erosion models are often simplified and require more knowledge on processes. Rill erosion is a small-scale but universally occurring phenomenon. Given its potential to concentrate into larger-scale erosion and its non-negligible contributions to soil loss, substantial research has been dedicated to understanding its processes. In this article, we conducted a holistic review of the major achievements in rill erosion research over the past few decades, mainly from the following perspectives: 1) Hydraulic parameters to describe rill development; 2) morphological indicators to represent rill morphology; 3) commonly used measuring methods for rill morphology and rill flow; and 4) advantages and limitations of rill erosion modelling. In each of the perspectives, we also identified the challenges faced by current rill erosion research. Concrete suggestions on the pressing needs to help advance rill erosion research in the future are further presented. [ABSTRACT FROM AUTHOR]

• Soil CO 2 emissions decreased exponentially with slope gradients. • Erosion-distributed water and nutrient responsible for slope dependent CO 2 emissions. • First study to parameterize the dependency of soil CO 2 emissions to slope gradients. Slope induced runoff and erosion processes redistribute water, soil and nutrients, thus potentially influence soil CO 2 emissions and perturb the carbon balances on sloping land. However, most of the previous studies on soil CO 2 emissions were conducted on flat land. In regions with complex terrains and fragmented fields with terraces, such as the Chinese Loess Plateau, it is particularly important to understand slope dependent soil CO 2 emissions. This requires investigations to unravel the relationship between soil erosional responses and CO 2 emissions on different slopes. In this study, erosion plots, set at angles of 0.5°, 5°, 10°, and 20°, were refilled with loess soils from local farmland on the Chinese Loess Plateau. Changes of soil properties and CO 2 emission rates were measured at three positions (upper, middle, lower) on each plot from October 2014 to September 2015. Our results show that greater runoff from the steeper slopes evidently depleted soil water and nutrients, directly responsible for the less soil CO 2 emissions. Furthermore, the average yearly soil CO 2 emissions decreased exponentially with slope gradients, from approximately 832.7 g m−2 yr−1 on the 0.5° slope, to 380.9 g m−2 yr−1 when the slope gradient was 20°. This not only proves the dependency of soil CO 2 emission to slope gradients, but also provides the fundamental dataset to develop an empirical model between slope gradients and soil CO 2 emissions. A coefficient β has been parameterized for the first time in this study to represent the sensitivity of soil CO 2 emissions to slope gradients. The model of slope-dependent CO 2 emissions identified in this study tentatively demonstrate non-negligible implications for global carbon fluxes from sloped and terraced field to the atmosphere. Further investigations on slope-scale carbon balances should test and integrate topography specific CO 2 emissions. [ABSTRACT FROM AUTHOR]