Abstract [Background] Ephemeral gullies (EG) are small channels eroded by concentrated flow. The traditional method of monitoring EG is the ruler method, by which the widths, depths and lengths of EGs are manually measured. Ridging, whereby elevated rows are created, is a commonly used tillage practice in China. EGs can develop in ridged croplands as furrows serve to concentrate runoff so that EGs develop perpendicular to rows as water spills over one ridge to the next furrow. In this case, the fluctuating relief induced by ridging causes difficulty in measurement of EG depth. Whether measurements are taken at ridge tops or in furrows, the measured depth cannot be used directly to calculate EG volume and must be calibrated to the EG depth that would have formed on a none-ridge (flat) land surface. Reports on the procedure and validity of calibration are limited. This study aims to establish an equation by which one can calibrate the depth measured from a ridge top (measured depth) to the corresponding depth for a none-ridge land surface case ( calibrated depth ), and understand the necessity of calibration. [Methods] Firstly, the cross-section of a ridge was established, whose shape was assumed to be an isosceles trapezoid. The distance from the ridge top to the EG bottom was measured, i. e. measured depth. Secondly, the ridge height was adjusted to that of a flat land surface. The distance from the newly adjusted land surface to the EG bottom was the calibrated depth. Thirdly, a calibration equation was established according to plane geometry knowledge. Fourthly, the calibration equation was applied to EGs in the Hebei-2 small watershed in the Heilongjiang Province to estimate the EG volume error in the non- calibration case. [Results] 1) The calibrated depth was a function of the measured depth and the morphologic characteristics of the ridges (height, top width and bottom width). 2) If the calibration was not used, the EG volume would be overestimated. The overestimation can be evaluated with relative error ratio (RER), which was positively correlated with the height and sharpness of the ridge and negatively correlated with EG depth. In the Hebei-2 watershed, the RER was 48% -75% when the EG was 5 cm deep and 5% - 8% when the EG was almost 50 cm deep. For all 51 EGs, the RER was 17%. Therefore, the calibration is necessary. [Conclusion] For EGs in ridged croplands, the measured depth can be calibrated by the equation developed in this study, with morphologic characteristics of the ridges as parameters. Without calibration, the EG depth and volume could be overestimated by up to 17% at the small watershed scale. Therefore, the established equation is suitable for this calibration, and the calibration is necessary, and even necessary for watersheds with high and sharp ridges and shallow EGs. We suggest that the results may be utilized for future EG surveying by more accurately calculating the significance of EG erosion.
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