Features of the Model

From GeoMod

Features of the model

1. This gully erosion model is based on using hypothetical surface having some general downward slope and some undulation.
2. The main equation of sediment capacity of cells is taken from article of Istanbulluoglu E., Tarboton D., Pack R., 2003. A sediment transport model for incision of gullies on steep topography. Water Resources Research Vol. 39, No. 4. From this article the following equation is used which relates the transport capacity to overland flow shear stress, which is further related to runoff rate, slope and drainage area. Qs = [K * inv(chiC) * (chiW) * (chiTou)^P * (d)^(1.5-P) * (1-TouC*inv(chiTou) * (r*A)^-Mtou*S^-Ntou)^P] * (r*A)^M * S^N where
   1. Qs is the sediment transport capacity
   2. K and P are the emperical parameters which are obtained after plotting dimensionless sediment transport rate and dimensionless shear stress. In this model the value of these parameters are taken as 20 and 3. These values are taken from the calibration performed by Istanbulluoglu E. et.al in their article based on the gullies in southwestern Idaho.
   3. ChiC, ChiW and ChiTou are the physical parameters of generic hydraulic variable such as C is shape constant, W is flow width and Tou is effective shear stress.
   4. d is the dominant grain size.
   5. TouC is the critical shear stress for incipient motion.
   6. r is the runoff rate. A is the upslope contributing area.
   7. S is the local slope.
   8. Mtou and Ntou are the constants M and N are variables based on the P, Mtou and Ntou.
   9. The gully incision rate is defined by T. It is the time required for the incision of the gully.
3. Values of most of the variables are taken as it is from the Istanbulluoglu's article.
4. Applying the above mention equation and specifying the rate of gully incision results in the long rill erosion in the topography.
5. To obtain the gully erosion, finite difference approximation equation is used. The concept depends upon the diffusion i.e, the amount of outflow from a cell is equal to sum of inflow and change in the volume of that cell. In other words, the change in the volume(height of the cell) is equal to the sediment transport to that cell from x and y direction and sediment transport out of that cell in x and y direction. A constant is used in the diffusion equation.
6. A while loop is used which calls the sediment transport equation and diffusion equation to number of times defined by the users.

Factors that effect the gully erosion model

1. The total number of cells and spacing between them for creating the hypothetical area are self.nx, self.ny, self.dx and self.dy resp. By changing these values the position of gully will also change.
2. General slope given to the topography is also user defined. By changing the slope value will also effect the location as well as the total erosion from the gully model.
3. The runoff rate as well as the gully incision rate will not only effect the amount of erosion and location of gully but also it will create numerical unstability in case these values are too high.
4. The values of K and P are obtained by calibration curve and depends on field values of sediment type, runoff rate, shear stress and other hydraulic parameters. These values may change from one gully system to another and will effect the location of gully initiation.
5. One of the major factor which is effecting the total erosion from the topography and initiation of the gully is the diffusion constant. There are higher chances of having numerical instability in case the value of this constant is large.
6. The last thing that can effect the total erosion from model is total number of times the sediment erosion equation and diffusion equation is called. The more number of times it will be called the more erosion it will cause.