Mathematical Methods of Assessing Gully

For more than half a century, soil erosion prediction and modeling technology has been used as a valuable tool in protective design, engineering plans and research development. This technology includes mathematical equations that calculate estimates of the dependent variables of erosion (soil losses, production and sediment) as a function of independent variables (four main factors: climate, soil, topography, and type of use). The parameters in these equations include exponential powers and coefficients that determine or modify the values ​​of the independent variables as part of mathematical calculations, some of which are empirical values ​​prepared according to basic data, while others have physical definitions associated with erosion processes. Mathematical symbols and logical sequence are among other features of mathematical models. In general, erosion mathematical models include regression-derived models, characteristic models, and process models. In addition to empirical methods, several mathematical models are presented concerning erosion, in all of which mass conservation law or the continuity equation are used as the controlling equation. These models include the dynamic and static models, the weep model, GULTEM and EGEM model, each of which is related to a particular type of gully and is applicable in certain conditions. Undoubtedly, the models introduced in this paper can not be considered as comprehensive models without any probable defects. Therefore, it is suggested that according to the climatic, geological, geomorphological, and ... characteristics, a suitable model be determined for assessing the rate of gully erosion in each region.